Exam-style Questions: Measurement

  1. Instructions for making a heart shaped cake:

    • Bake a square cake of side 20cm.
    • Bake a round cake of radius 10cm.
    • Cut the round cake in half.
    • Join the two halves to the square cake, as shown in the diagram.

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    a) Find the area of the heart-shape. State the units of your answer.

    (4 marks)

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    A red ribbon is fixed around the sides of the heart-shaped cake with the ends overlapping by 3cm.

    b) Find the length of the ribbon required.

    (3 marks)

    (Marks available: 7)

    Answer

    Answer outline and marking scheme for question: 1

    a) 714 to 714.2 cm2

    (4 marks)

    b) 105.8 to 106 cm

    (3 marks)

    (Marks available: 7)

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    (i) What is the volume of the cuboid?

    (1 mark)

    (ii) What is the area of the shaded top of the cuboid?

    (1 mark)

    (Marks available: 2)

    Answer

    Answer outline and marking scheme for question: 2

    (i) 40cm3

    (ii) 20cm2

    (Marks available: 2)

  3. A rectangular photograph, 12cm long and 8cm wide, fits into a rectangular frame so that there is a border 4cm wide all the way round it.

    Use calculations to show whether or not the two rectangles are similar.

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    (Marks available: 4)

    Answer

    Answer outline and marking scheme for question: 3

    Using corresponding ratios/fractions, compare the sides of the pictures, which should show the pictures as not similar.

    (Marks available: 4)

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    A hemispherical bowl has a radius of 30cm.

    a) (i) Calculate the volume of the bowl. Leave your answer as a multiple of π.

    (2 marks)

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    (ii) A cylinder of radius 20cm and height h cm has the same volume as the bowl. Calculate the value of h.

    (2 marks)

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    b) Calculate the radius of the surface of the water.

    (3 marks)

    (Marks available: 7)

    Answer

    Answer outline and marking scheme for question: 4

    a)(i) 18000 cm3

    (ii) 45

    b) 24

    (Marks available: 7)