# 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. 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)

2. (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)

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. (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)

4. 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) 