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GCSE Maths · Higher · Chapter 9: Length, area and volume · Lesson 3

Prisms and cylinders

Grades 5–7About 55 minutesCalculator allowed37 marks
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NameClassDate
A

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

  1. A1
    Needed today

    A trapezium has parallel sides 6 cm and 9 cm, 12 cm apart. Find its area.

    [1 mark]
    Answer
  2. A2
    From chapter 9

    A circle has radius 7 cm. Find its circumference in terms of .

    [1 mark]
    Answer
  3. A3
    Key Stage 3

    Write 2 hours 45 minutes in hours, as a decimal.

    [1 mark]
    Answer
  4. A4
    Key Stage 3

    Round to 2 significant figures.

    [1 mark]
    Answer
B

Example, then your turn

Grades 5–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

Work out the volume of the triangular prism.

10 cm7 cm15 cm
Hint Volume of a prism area of cross-section length.
  1. B1

    Work out the volume of the prism.

    [2 marks]
    8 cm9 cm12 cm
    Answer
Example 2

Work out the volume of the cylinder. Give your answer to significant figures.

6 cm7 cm
Hint A cylinder is a prism with a circle as its cross-section.
  1. B2

    Work out the volume of the cylinder. Give your answer to significant figures.

    [2 marks]
    4.5 cm12 cm
    Answer
C

Practice

Grades 5–7
  1. C1

    The cross-section of this prism is a right-angled triangle. Work out its total surface area.

    [4 marks]
    12 cm9 cm14 cm
    Not drawn accurately
    Answer
  2. C2

    The cylinder has a volume of cm. Work out its radius, . Give your answer to decimal place.

    [3 marks]
    r9 cm
    Not drawn accurately
    Answer
  1. C3

    The prism has an L-shaped cross-section. Work out its volume.

    [3 marks]
    8 cm6 cm3 cm3 cm12 cm
    Not drawn accurately
    Answer
  2. C4

    A metal pipe is cm long. Its end is the ring shown. Work out the volume of metal. Give your answer to significant figures.

    [3 marks]
    5 cm4 cm
    Answer
D

Exam-style questions

Grades 6–7
  1. D1

    Soup is sold in two sizes of cylindrical tin. Tin A costs p and Tin B costs £. Sam says, "Tin A is better value because it is cheaper."

    Show that Sam is wrong.

    [4 marks]
    4 cm9 cmTin A5 cm11 cmTin B
    Not drawn accurately
  1. D2

    A cuboid tank cm by cm by cm is full of water. All the water is poured into an empty cylindrical tank of radius cm and height cm.

    50 cm30 cm40 cm20 cm45 cm
    Not drawn accurately
    (a)

    Show that the water overflows, and work out how much overflows, in litres. Give your answer to decimal place.

    [5 marks]
    Answer
    (b)

    The cylindrical tank has a base but no lid. Work out the area of its outside surface. Give your answer to significant figures.

    [3 marks]
    Answer
    Total for D2: 8 marks
E

Extension

Grade 7 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

  1. E1

    A cylinder fits exactly inside a cube of side cm, touching all six faces. What percentage of the cube is empty space? Give your answer to significant figures.

    [4 marks]
    10 cmView from above
    Hint 1 · What to try

    The cylinder is as tall as the cube and as wide as the cube. What are its radius and height?

    Hint 2 · The first line

    The radius is cm and the height is cm, so the cylinder holds cm.

    Hint 3 · The full method

    Empty space cm. Write this as a percentage of .

    Answer
F

How did it go?

Colour one circle on each line.
Not yetNearlyYes
I can work out the volume of a prism and a cylinder.
I can work out surface areas and work back from a volume to a missing length.
I can use these in problems with containers, units and value for money.

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