Free textbooks › Year 8 Maths textbook
KS3 Maths · Year 8Chapter 10 · Area and volume of prisms and cylinders
Year 8 · Chapter 10

Area and volume of prisms and cylinders

By the end of this chapter you will be able to

  • Find the area of a trapezium and of a compound shape made from rectangles and triangles
  • Find the area and circumference of a circle, and give answers in terms of pi
  • Find the volume of a cuboid and of a triangular prism, using the area of the cross-section
  • Find the volume and curved surface area of a cylinder, and give answers in terms of pi
  • Find the surface area of a cuboid, and convert square and cubic units such as m2 to cm2

You should already know

  • Area of rectangles, triangles and parallelograms, and the formula for the area of a rectangle (Year 7)
  • Multiplying decimals and whole numbers, and the square of a number (Year 7 and Year 8, Chapter 9)
  • Units of length, and the relationship between cm and m (Year 7)

Where this leads

  • Circle theorems, sectors, arcs and surface areas of cones and spheres (Year 9 and GCSE)
  • Volume and surface area of more complex solids, and the use of formulae (Year 9)
  • Similar shapes and the effect of a scale factor on area and volume (Year 9)

National Curriculum for England, Key Stage 3 mathematics, Year 8. Content: Use area formulae for trapeziums, circles and compound shapes, and convert units of area, Find the volume of a cuboid, and of a prism with a uniform cross-section, as the area of the cross-section times the length, Find the volume and curved surface area of a cylinder, using pi, Find the surface area of a cuboid or a prism.

Exercise P  Do you remember?

Non-calculator
1
FWhat is the area of a rectangle that is 8 cm long and 3 cm wide?
2
FWork out 6 × 4 × 2.
3
FWhat is 1 m in centimetres?
4
FWork out 32 × 2.
5
FThe perimeter of a square with side 5 cm is how many centimetres?
10.1

Area of trapeziums and compound shapes

Year 8
Use area formulae for trapeziums and compound shapes
Video lesson: Area of trapeziums and compound shapesComing soon
A garden has a flower bed shaped like a trapezium. Ben wants to know the area, so he can work out how many bags of compost to buy.

A trapezium has two parallel sides. Its area is the average of the parallel sides, multiplied by the height (the perpendicular distance between them).

A = (a + b) ÷ 2 × h, where a and b are the parallel sides.

A compound shape is made from simpler shapes. Split it into rectangles and triangles, find the area of each part, then add them.

Key ideas

  • Trapezium area: (a + b) ÷ 2 × h.
  • The height is perpendicular to the parallel sides, not the slanted side.
  • For a compound shape, split it into parts and add the areas.
  • If part of a shape is missing, subtract its area from the whole.
Worked example 10.1.1
Find the area of a trapezium with parallel sides 5 cm and 9 cm, and height 4 cm.

Method. The area of a trapezium is the average of the two parallel sides, times the height.

  1. Write the formula. Area = (a + b) ÷ 2 × h.
    A = (a + b) ÷ 2 × h
  2. Add the parallel sides. The parallel sides are 5 cm and 9 cm.
    5 + 9 = 14
  3. Halve and multiply by the height. Half of 14 is 7, then multiply by 4 cm.
    7 × 4 = 28
  4. Write the answer.
    28 cm2

Check. The average of 5 and 9 is 7.0, and 7.0 × 4 = 28.0.

Watch out. Use the perpendicular height, not the slanted side.

Worked example 10.1.2
A shape is made of a rectangle 8 cm by 3 cm and a rectangle 4 cm by 5 cm. Find its total area.

Method. Find the area of each rectangle, then add them.

  1. Area of the first rectangle. 8 × 3 = 24 cm2.
    24
  2. Area of the second rectangle. 4 × 5 = 20 cm2.
    20
  3. Add the areas. 24 + 20 = 44.
    44 cm2

Check. The two rectangles do not overlap, so their areas add.

Worked example 10.1.3
A rectangle 10 cm by 6 cm has a corner square of side 2 cm cut out. Find the area that is left.

Method. Find the area of the whole rectangle, then subtract the cut-out part.

  1. Area of the rectangle. 10 × 6 = 60 cm2.
    60
  2. Area of the cut-out. 2 × 2 = 4 cm2.
    4
  3. Subtract. 60 − 4 = 56.
    56 cm2

Check. 56 + 4 = 60.

Watch out

Watch out: use the perpendicular height. A slanted side of a trapezium is longer than the height, so using it gives the wrong area.

Exam tip

Exam tip. Write the formula, then put in the numbers in order. Give the units in your final answer.

Exercise 10A  Area of trapeziums and compound shapes

Non-calculator
1
FA trapezium has parallel sides 5 cm and 9 cm, and height 4 cm. Find its area.
2
FA trapezium has parallel sides 6 cm and 10 cm, and height 5 cm. Find its area.
3
FA trapezium has parallel sides 3 cm and 7 cm, and height 6 cm. Find its area.
4
FA trapezium has parallel sides 8 cm and 12 cm, and height 3 cm. Find its area.
5
FA trapezium has parallel sides 4 cm and 10 cm, and height 7 cm. Find its area.
6
FA trapezium has parallel sides 2 cm and 8 cm, and height 5 cm. Find its area.
7
FA trapezium has parallel sides 7 cm and 11 cm, and height 2 cm. Find its area.
8
FA shape is made from a rectangle 8 cm by 3 cm and a rectangle 4 cm by 5 cm. Find its total area.
9
PSA rectangle 10 cm by 6 cm has a square of side 2 cm cut from one corner. Find the area of the shape that is left.
10
PSAn L-shape is made from a rectangle 12 cm by 4 cm, and a rectangle 3 cm by 6 cm joined on. Find its total area.
11
PSA trapezium-shaped flower bed has parallel sides of 4 cm and 8 cm, and a height of 3 cm. Find its area.
12
RAli says that a trapezium with parallel sides 5 cm and 9 cm, and slanted side 6 cm, has area found by using 6 instead of the height. Is Ali right? Explain.
13
RA shape has area 45 cm2 made from a rectangle 9 cm by 5 cm. Explain why adding a second part of 2 cm2 would give 47 cm2.
14
PSA trapezium has area 36 cm2, parallel sides 4 cm and 8 cm. Find its height.
10.2

Area and circumference of a circle

Year 8
Use the area and circumference of a circle, and give answers in terms of pi
Video lesson: Area and circumference of a circleComing soon
A round table has a radius of 5 metres. A designer draws a circle to show where the tablecloth will reach, and she needs its area and the distance around its edge.

The radius r is the distance from the centre to the edge. The diameter is twice the radius.

The area of a circle is π r2. The circumference (distance round) is 2π r.

Leave the answer in terms of π (for example 25π) when you are asked for an exact answer, so you do not need a calculator.

Key ideas

  • Area of a circle = π r2.
  • Circumference = 2π r = π d.
  • Square the radius before you multiply by π.
  • Use the radius, not the diameter, in the area formula.
Worked example 10.2.1
Find the area of a circle with radius 6 cm. Give your answer in terms of π.

Method. The area of a circle is π r2. Leave the answer in terms of π.

  1. Write the formula. Area = π r2.
    A = π r2
  2. Square the radius. The radius is 6 cm, so r2 = 6 × 6.
    62 = 36
  3. Multiply by π. Leave π in the answer.
    A = 36π
  4. Write the answer.
    36π cm2

Check. If you use π = 3.14, the area is about 113 cm2.

Watch out. Square the radius first, not the diameter. The diameter is twice the radius.

Worked example 10.2.2
Find the circumference of a circle with radius 4 cm. Give your answer in terms of π.

Method. The circumference of a circle is 2π r. Leave the answer in terms of π.

  1. Write the formula. Circumference = 2π r.
    C = 2π r
  2. Put in r. The radius is 4 cm.
    2 × π × 4
  3. Multiply. Multiply the numbers, and keep π.
    C = 8π
  4. Write the answer.
    8π cm

Check. The circumference is about 3 times the diameter (8 cm), so about 24 cm.

Watch out. Use the radius with the formula 2πr, or the diameter with πd.

Worked example 10.2.3
Find the area of a semicircle with radius 6 cm, in terms of π.

Method. A semicircle is half a circle, so its area is half the area of the full circle.

  1. Find the area of the full circle. Area = π × 62 = 36π.
    36π
  2. Halve it. A semicircle is half the circle.
    36π ÷ 2 = 18π
  3. Write the answer.
    18π cm2

Check. 18π is half of 36π.

Watch out

Watch out: the area is π r2, not 2π r. Square the radius first, and do not use the diameter in the area formula.

Exam tip

Exam tip. If a question says “give your answer in terms of π”, leave the π in the answer. Do not write a decimal.

Exercise 10B  Area and circumference of circles

Non-calculator
1
FFind the area of a circle with radius 3 cm. Give your answer in terms of π.
2
FFind the area of a circle with radius 5 cm. Give your answer in terms of π.
3
FFind the area of a circle with radius 6 cm. Give your answer in terms of π.
4
FFind the area of a circle with radius 10 cm. Give your answer in terms of π.
5
FFind the area of a circle with radius 4 cm. Give your answer in terms of π.
6
FFind the area of a circle with radius 7 cm. Give your answer in terms of π.
7
FFind the circumference of a circle with radius 4 cm. Give your answer in terms of π.
8
FFind the circumference of a circle with radius 7 cm. Give your answer in terms of π.
9
FFind the circumference of a circle with radius 5 cm. Give your answer in terms of π.
10
PSFind the area of a semicircle with radius 6 cm. Give your answer in terms of π.
11
PSA round table has radius 5 cm. Find the distance round the table, in terms of π.
12
PSA circle has a diameter of 8 cm. Find its area, in terms of π.
13
RAli says that the area of a circle with radius 3 cm is 6π cm2. Is Ali right? Explain.
14
RExplain the difference between the area and the circumference of a circle with radius 5 cm. Accept any answer that gives 25π and 10π with units.
15
PSA circular pond has a radius of 10 cm. Find the area of the pond, in terms of π.
10.3

Volume of cuboids and prisms

Year 8
Find the volume of a cuboid, and of a prism with a uniform cross-section, as the area of the cross-section times the length
Video lesson: Volume of cuboids and prismsComing soon
A box for a gift is a cuboid, 5 cm long, 4 cm wide and 3 cm high. Mia wants to know how much space is inside, so that she can check how many sweets will fit.

The volume of a cuboid is length × width × height.

A prism has the same cross-section all the way along its length. Its volume is area of the cross-section × length.

For a triangular prism, the cross-section is a triangle, with area ½ × base × height.

Key ideas

  • Cuboid volume = length × width × height.
  • Prism volume = area of the cross-section × length.
  • Volume is measured in cubic units, such as cm3.
  • For a triangular cross-section, the area is ½ × base × height.
Worked example 10.3.1
Find the volume of a cuboid that is 5 cm long, 4 cm wide and 3 cm high.

Method. The volume of a cuboid is length × width × height.

  1. Write the formula. Volume = length × width × height.
    V = l × w × h
  2. Put in the numbers. The sides are 5 cm, 4 cm and 3 cm.
    5 × 4 × 3
  3. Multiply. Multiply the three numbers.
    20 × 3 = 60
  4. Write the answer.
    60 cm3

Check. Check: 60 ÷ 3 = 20, which is the area of the base.

Watch out. Write the answer in cubic units, cm3.

Worked example 10.3.2
A prism has a cross-section of area 12 cm2 and length 10 cm. Find its volume.

Method. For a prism, the volume is the area of the cross-section × the length.

  1. Find the area of the cross-section. This is the area of the end face of the prism.
    area = 12 cm2
  2. Multiply by the length. The prism is 10 cm long.
    12 × 10 = 120
  3. Write the answer.
    120 cm3

Check. Check: 120 ÷ 10 = 12, the cross-section area.

Watch out. Use the area of the cross-section (the end), not the area of the long face.

Worked example 10.3.3
A triangular prism has a cross-section triangle with base 6 cm and height 4 cm, and length 10 cm. Find its volume.

Method. First find the area of the triangular cross-section, then multiply by the length.

  1. Find the area of the cross-section. Area of a triangle = ½ × base × height.
    ½ × 6 × 4 = 12 cm2
  2. Multiply by the length. The prism is 10 cm long.
    12 × 10 = 120
  3. Write the answer.
    120 cm3

Check. 12 ÷ 10 would give the cross-section again.

Watch out

Watch out: the volume is in cubic units, cm3. Do not give a volume with squared units.

Exam tip

Exam tip. For a prism, write the area of the cross-section first. Then multiply by the length. Check the units.

Exercise 10C  Volume of cuboids and prisms

Non-calculator
1
FA cuboid is 5 cm long, 4 cm wide and 3 cm high. Find its volume.
2
FA cuboid is 8 cm long, 2 cm wide and 7 cm high. Find its volume.
3
FA cuboid is 10 cm long, 10 cm wide and 10 cm high. Find its volume.
4
FA cuboid is 6 cm long, 5 cm wide and 2 cm high. Find its volume.
5
FA cuboid is 3 cm long, 3 cm wide and 9 cm high. Find its volume.
6
FA cuboid is 7 cm long, 4 cm wide and 4 cm high. Find its volume.
7
FA prism has a cross-section of area 12 cm2 and length 10 cm. Find its volume.
8
FA prism has a cross-section of area 20 cm2 and length 5 cm. Find its volume.
9
FA prism has a cross-section of area 9 cm2 and length 7 cm. Find its volume.
10
FA prism has a cross-section of area 15 cm2 and length 4 cm. Find its volume.
11
PSA triangular prism has a cross-section triangle with base 6 cm and height 4 cm, and length 10 cm. Find its volume.
12
PSA box is 20 cm long, 15 cm wide and 8 cm high. How many cubes of side 1 cm fit inside it?
13
RAli says the volume of a cuboid 2 cm by 3 cm by 4 cm is 9 cm3. Is Ali right? Explain.
14
PSA water tank in the shape of a prism has a cross-section of 0.5 m2 and a length of 4 m. Find its volume in m3.
15
PSA cuboid has a volume of 60 cm3, length 5 cm and width 4 cm. Find its height.
16
RA prism is 12 cm long, with a cross-section of area 7 cm2. Find its volume and explain why you multiply by the length.
10.4

Volume and curved surface area of a cylinder

Year 8
Find the volume and curved surface area of a cylinder, using pi
Video lesson: Volume and curved surface area of a cylinderComing soon
A cylindrical can has a radius of 3 cm and a height of 5 cm. Sam wants to know how much drink it holds, and how much label he needs for the curved side.

A cylinder is a prism with a circular cross-section.

Its volume is the area of the circle times the height: π r2 h.

Its curved surface area is the curved side unrolled into a rectangle: 2π r h.

Key ideas

  • Volume of a cylinder = π r2 h.
  • Curved surface area = 2π r h.
  • Give the answer in terms of π if you are not using a calculator.
  • Square the radius first, then multiply by the height.
Worked example 10.4.1
Find the volume of a cylinder with radius 3 cm and height 5 cm. Give your answer in terms of π.

Method. The volume of a cylinder is π r2 h. Leave the answer in terms of π.

  1. Write the formula. Volume = (area of circle) × height = π r2 h.
    V = π r2 h
  2. Put in the numbers. The radius is 3 cm and the height is 5 cm.
    π × 32 × 5
  3. Work out the powers and multiply. 32 = 9, then multiply by 5.
    9 × 5 = 45
  4. Write the answer.
    45π cm3

Check. If you use π = 3.14, the volume is about 141 cm3.

Watch out. Square the radius before you multiply by the height.

Worked example 10.4.2
Find the curved surface area of a cylinder with radius 3 cm and height 5 cm. Give your answer in terms of π.

Method. The curved surface area of a cylinder is 2π r h. Leave the answer in terms of π.

  1. Write the formula. The curved surface is a rectangle: its length is the circumference, 2π r.
    CSA = 2π r h
  2. Put in the numbers. The radius is 3 cm and the height is 5 cm.
    2 × π × 3 × 5
  3. Multiply. Multiply the numbers, and keep π.
    CSA = 30π
  4. Write the answer.
    30π cm2

Check. The curved surface area is the area of the rectangle made by unrolling the curved side.

Worked example 10.4.3
A cylinder has radius 2 cm and height 10 cm. Find its volume in terms of π.

Method. The volume of a cylinder is π r2 h. Leave the answer in terms of π.

  1. Write the formula. Volume = (area of circle) × height = π r2 h.
    V = π r2 h
  2. Put in the numbers. The radius is 2 cm and the height is 10 cm.
    π × 22 × 10
  3. Work out the powers and multiply. 22 = 4, then multiply by 10.
    4 × 10 = 40
  4. Write the answer.
    40π cm3

Check. If you use π = 3.14, the volume is about 126 cm3.

Watch out. Square the radius before you multiply by the height.

Watch out

Watch out: the curved surface area is 2π r h, and the volume is π r2 h. The volume has the squared radius.

Exam tip

Exam tip. Write the formula you are using before you put in the numbers. It shows the method, even if the arithmetic slips.

Exercise 10D  Cylinders

Non-calculator
1
FA cylinder has radius 3 cm and height 5 cm. Find its volume, in terms of π.
2
FA cylinder has radius 2 cm and height 10 cm. Find its volume, in terms of π.
3
FA cylinder has radius 4 cm and height 3 cm. Find its volume, in terms of π.
4
FA cylinder has radius 5 cm and height 2 cm. Find its volume, in terms of π.
5
FA cylinder has radius 1 cm and height 9 cm. Find its volume, in terms of π.
6
FA cylinder has radius 6 cm and height 2 cm. Find its volume, in terms of π.
7
FA cylinder has radius 3 cm and height 5 cm. Find its curved surface area, in terms of π.
8
FA cylinder has radius 5 cm and height 4 cm. Find its curved surface area, in terms of π.
9
FA cylinder has radius 2 cm and height 6 cm. Find its curved surface area, in terms of π.
10
FA cylinder has radius 4 cm and height 4 cm. Find its curved surface area, in terms of π.
11
PSA can has radius 4 cm and height 10 cm. How much does it hold? Give your answer in terms of π.
12
PSA label covers the curved side of a can with radius 3 cm and height 12 cm. Find the area of the label, in terms of π.
13
PSA cylinder has a volume of 45π cm3 and height 5 cm. Find its radius. Explain your method.
14
RAli says that the volume of a cylinder with radius 2 cm and height 3 cm is 12π cm3. Is Ali right? Show your working.
15
RTwo cylinders have the same height, 5 cm. One has radius 2 cm and the other radius 4 cm. How many times bigger is the volume of the second? Explain.
10.5

Surface area of a cuboid and converting units

Year 8
Find the surface area of a cuboid or prism, Convert units of area and volume
Video lesson: Surface area of a cuboid and converting unitsComing soon
A builder paints the outside of a shed. The shed is a cuboid, so Ali finds the surface area by adding the areas of all six faces. He also needs to change square metres to square centimetres, because the paint tin uses cm2.

The surface area of a cuboid is the total area of all six faces. Opposite faces are equal, so find three pairs and add them.

To change units: 1 m = 100 cm. Because area has two dimensions, 1 m2 = 100 × 100 = 10 000 cm2. Because volume has three dimensions, 1 m3 = 100 × 100 × 100 = 1 000 000 cm3.

Key ideas

  • Surface area of a cuboid: add the areas of the six faces, in three pairs.
  • 1 m2 = 10 000 cm2.
  • 1 m3 = 1 000 000 cm3.
  • Multiply by 100 for each dimension when changing units of volume.
Worked example 10.5.1
Find the surface area of a cuboid that is 2 cm by 3 cm by 4 cm.

Method. Find the area of each of the six faces, then add them. Opposite faces are the same.

  1. Find the area of the top and bottom. Two faces, each 2 × 3.
    2 × 6 = 12
  2. Find the area of the front and back. Two faces, each 3 × 4.
    2 × 12 = 24
  3. Find the area of the two ends. Two faces, each 2 × 4.
    2 × 8 = 16
  4. Add the areas. Add the areas of all six faces.
    12 + 24 + 16 = 52
  5. Write the answer.
    52 cm2

Check. There are six faces in pairs. Each pair has the same area.

Worked example 10.5.2
Change 2 m2 to cm2.

Method. 1 m is 100 cm, so 1 m2 is 100 × 100 = 10 000 cm2. Multiply by 10 000 to change m2 to cm2.

  1. Write the conversion. 1 m2 = 100 cm × 100 cm.
    1 m2 = 10 000 cm2
  2. Multiply. Multiply 2 by 10 000.
    2 × 10 000 = 20000
  3. Write the answer.
    20,000 cm2

Check. A square metre is a square of side 1 m, which is 100 cm by 100 cm.

Watch out. Do not multiply by 100 for an area. It is 10 000, because there are two dimensions.

Worked example 10.5.3
Change 3 m3 to cm3.

Method. Each dimension is 100 times bigger in cm, so multiply by 100 three times.

  1. Write the conversion. 1 m3 = 100 × 100 × 100 cm3.
    1 m3 = 1 000 000 cm3
  2. Multiply. 3 × 1 000 000 = 3 000 000.
    3 000 000
  3. Write the answer.
    3 000 000 cm3

Check. 1 000 000 ÷ 1 000 000 = 1 m3.

Watch out

Watch out: 1 m2 is 10 000 cm2, not 100 cm2. Multiplying by 100 only works for length, not for area.

Exam tip

Exam tip. When you convert units, write the conversion first, for example 1 m2 = 10 000 cm2. Then multiply.

Exercise 10E  Surface area and units

Non-calculator
1
FFind the surface area of a cuboid that is 2 cm by 3 cm by 4 cm.
2
FFind the surface area of a cuboid that is 5 cm by 5 cm by 2 cm.
3
FFind the surface area of a cuboid that is 10 cm by 4 cm by 3 cm.
4
FFind the surface area of a cuboid that is 6 cm by 2 cm by 1 cm.
5
FFind the surface area of a cuboid that is 3 cm by 3 cm by 3 cm.
6
FFind the surface area of a cuboid that is 4 cm by 2 cm by 7 cm.
7
FChange 2 m2 to cm2.
8
FChange 0.5 m2 to cm2.
9
FChange 3 m2 to cm2.
10
FChange 3 m3 to cm3.
11
PSA cuboid is 1 m long, 50 cm wide and 20 cm high. Write the length, width and height in cm, then find the volume in cm3.
12
PSA box is 4 cm by 3 cm by 2 cm. Find its total surface area.
13
PSA tin of paint covers 5 m2. How many cm2 does it cover?
14
RAli says that 1 m2 is 100 cm2. Is Ali right? Explain.
15
RTwo cuboids both have a volume of 24 cm3. One is 2 cm by 3 cm by 4 cm. Ali says the surface areas must be the same. Is Ali right? Explain.

Chapter summary

SkillMethod
Trapezium(a + b) ÷ 2 × h
CircleArea π r2; circumference 2π r
PrismVolume = area of cross-section × length
CylinderVolume π r2 h; curved surface area 2π r h
CuboidVolume = l × w × h; surface area = 2(lw + wh + lh)
Units1 m2 = 10 000 cm2; 1 m3 = 1 000 000 cm3

Can you…?

  • I can find the area of a trapezium and of a compound shape
  • I can find the area and circumference of a circle, in terms of π
  • I can find the volume of a cuboid and of a prism
  • I can find the volume and curved surface area of a cylinder, in terms of π
  • I can find the surface area of a cuboid
  • I can convert units of area and volume

Key terms

trapezium
a quadrilateral with one pair of parallel sides
prism
a solid with the same cross-section all the way along its length
cross-section
the shape you see when a solid is cut straight across
cylinder
a prism with a circular cross-section
surface area
the total area of all the faces of a solid
volume
the amount of space a solid takes up
pi
the ratio of the circumference of a circle to its diameter, written as π

Exercise 10Z  Check-up

Non-calculator
1
Find the area of a trapezium with parallel sides 6 cm and 10 cm, and height 5 cm.
2
Find the area of a circle with radius 9 cm, in terms of π.
3
Find the circumference of a circle with radius 6 cm, in terms of π.
4
Find the volume of a cuboid 6 cm long, 5 cm wide and 2 cm high.
5
A prism has a cross-section of area 15 cm2 and length 8 cm. Find its volume.
6
Find the volume of a cylinder with radius 2 cm and height 7 cm, in terms of π.
7
Find the curved surface area of a cylinder with radius 4 cm and height 3 cm, in terms of π.
8
Find the surface area of a cuboid 5 cm by 2 cm by 3 cm.
9
Change 4 m2 to cm2.
10
A trapezium has area 30 cm2 and parallel sides 5 cm and 7 cm. Find its height.

Total 31 marks. Allow about 31 minutes.

Exercise 10X  Exam-style questions

Non-calculator
1
FFind the area of a trapezium with parallel sides 7 cm and 13 cm, and height 6 cm.[2 marks]
2
FA circle has a radius of 5 cm. Find its circumference, in terms of π.[2 marks]
3
FFind the volume of a triangular prism with a cross-section of area 9 cm2 and length 12 cm.[2 marks]
4
FA cylinder has radius 3 cm and height 8 cm. Find its volume, in terms of π.[3 marks]
5
FA cylinder has radius 5 cm and height 4 cm. Find its curved surface area, in terms of π.[3 marks]
6
FFind the surface area of a cuboid 4 cm by 3 cm by 10 cm.[3 marks]
7
FA swimming pool is a cuboid 10 m long, 5 m wide and 2 m deep. Find its volume in m3.[2 marks]
8
FChange 2.5 m3 to cm3.[3 marks]
9
FA cylindrical tin has a diameter of 8 cm and height 10 cm. Find its volume, in terms of π.[4 marks]
10
FA prism has a cross-section which is a triangle with base 8 cm and height 5 cm. The prism is 6 cm long. Find its volume.[3 marks]
11
FA cuboid has surface area 52 cm2 and sides 2 cm, 3 cm and h cm. Find h, by writing and solving an equation.[4 marks]
← Chapter 9: Pythagoras and anglesChapter 11: Transformations and similarity →

Want a tutor to go through this chapter with your child?

Same tutor, same time, every week, live online. The first session is a free introduction.

💬 Book a Free Intro on WhatsApp
Chat on WhatsApp