Exam-style Questions: Measurement
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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.
a) Find the area of the heart-shape. State the units of your answer.
(4 marks)
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 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 outline and marking scheme for question: 2
(i) 40cm3
(ii) 20cm2
(Marks available: 2)
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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.
(Marks available: 4)
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)
(ii) A cylinder of radius 20cm and height h cm has the same volume as the bowl. Calculate the value of h.
(2 marks)
b) Calculate the radius of the surface of the water.
(3 marks)
(Marks available: 7)
Answer outline and marking scheme for question: 4
a)(i) 18000 cm3
(ii) 45
b) 24
(Marks available: 7)