Examstyle Questions: Measurement

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 heartshape. State the units of your answer.
(4 marks)
A red ribbon is fixed around the sides of the heartshaped 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 cm^{2}
(4 marks)
b) 105.8 to 106 cm
(3 marks)
(Marks available: 7)

(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) 40cm^{3}
(ii) 20cm^{2}
(Marks available: 2)

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)

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 cm^{3}
(ii) 45
b) 24
(Marks available: 7)