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GCSE Maths · Higher · Chapter 9: Length, area and volume · Lesson 4

Pyramids, cones and spheres

Grades 5–7About 55 minutesCalculator allowed35 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 prism has cross-section 21 cm and length 11 cm. Find its volume.

    [1 mark]
    Answer
  2. A2
    From chapter 5

    A block has mass 70 g and volume 10 cm. Find its density.

    [1 mark]
    Answer
  3. A3
    From chapter 9

    A parallelogram has base 6 cm and perpendicular height 5 cm. Find its area.

    [1 mark]
    Answer
  4. A4
    Key Stage 3

    A bag holds 2 red and 3 blue counters. Find P(red).

    [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

A pyramid has a rectangular base cm by cm and a vertical height of cm. Work out its volume.

9 cm4 cm
Hint Volume of a pyramid area of base height.
  1. B1

    A pyramid has a square base of side cm and a vertical height of cm. Work out its volume.

    [2 marks]
    7 cm7 cm
    Answer
Example 2

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

4 cm9 cm
Hint Volume of a cone , a third of the cylinder.
  1. B2

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

    [2 marks]
    3.5 cm10 cm
    Answer
C

Practice

Grades 5–7
  1. C1

    A ball has a diameter of cm. Work out its surface area. Give your answer to significant figures.

    [3 marks]
    22 cm
    Answer
  2. C2

    A sphere has a volume of cm. Work out its radius. Give your answer to decimal place.

    [3 marks]
    Answer
  1. C3

    A cone has a radius of cm and a slant height of cm. Work out its volume. Give your answer to significant figures.

    [3 marks]
    6 cm10 cm
    Not drawn accurately
    Answer
  2. C4

    A bowl is a hemisphere with an inside radius of cm. How many litres does it hold? Give your answer to significant figures.

    [3 marks]
    12 cm
    Answer
D

Exam-style questions

Grades 6–7
  1. D1

    A cone has radius cm and vertical height cm. Jo says, "The curved surface area is cm."

    Show that Jo is wrong, and work out the correct curved surface area.

    [3 marks]
    8 cm15 cm
    Not drawn accurately
    Answer
  1. D2

    A solid is a cone with a hemisphere on top, both of radius cm. The cone is cm tall.

    9 cm3.5 cm
    Not drawn accurately
    (a)

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

    [4 marks]
    Answer
    (b)

    Work out its outside surface area. Give your answer to significant figures.

    [4 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 bucket is a cone with its tip cut off. Its base radius is cm, its top radius cm and its height cm. How many litres does it hold, to significant figures?

    [4 marks]
    16 cm9 cm3 cm
    Hint 1 · What to try

    Carry the sloping sides down until they meet: a big cone with a small cone cut off.

    Hint 2 · The first line

    The radius triples, so the whole cone is times as tall as the small one: cm and cm.

    Hint 3 · The full method

    Bucket cm. Change cm to litres.

    Answer
F

How did it go?

Colour one circle on each line.
Not yetNearlyYes
I can work out the volume of a pyramid, a cone and a sphere.
I can use the slant height for a cone's curved surface, and work back from a volume.
I can work with solids made from more than one shape.

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