O-LevelMathematicsMensuration4024/22 · May/June 2020 · Q88 Marks
A birthday cake is in the shape of a cylinder. There are two layers of cake and one layer of icing. Each layer of cake has radius 10 cm and height 3 cm. The icing, between the two layers of cake, has radius 10cm and height 12mm.
- (a)[Figure 8.1] Calculate the volume of icing in the birthday cake. Give your answer in cm³.[2]
- (b)The top and curved surface of the birthday cake are now covered with chocolate. Calculate the area of the birthday cake that is covered with chocolate.[3]
- (c)[Figure 8.2] Anil has a slice of this chocolate-covered birthday cake. His slice is a prism of height 7.5 cm. The top of the cake is a sector, radius 10.3 cm and angle x°. The volume of his slice is 200 cm³. Calculate the value of x.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [2] (a) 376.99 to 377.04
- [2] M1 for π× 10² × figs12
- [3] (b) 767 or 766.5 to 766.6...
- [3] M2 for π× 10² + π× 2 × 10 × (3 + 3 + figs 12)
- [3] M1 for π× 10² or π× 2 × 10 × (3 + 3 + figs 12)
- [3] (c) 28.79 to 28.80...
- [3] M2 for 200 = x/360 × π× 10.3² × 7.5 or M1 for x/360 ×kπ used
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →