O-LevelMathematicsMensuration4024/22 · Oct/Nov 2015 · Q47 Marks
[The volume of a sphere is (4/3)πr³]
- (a)(i)A spoon used for measuring in cookery consists of a hemispherical bowl and a handle. The internal volume of the hemispherical bowl is 20 cm³. The handle is of length 5 cm. Find the internal radius of the hemispherical bowl.[2]
- (a)(ii)The hemispherical bowl of a geometrically similar spoon has an internal volume of 50cm³. Find the length of its handle.[2]
- (b)[The surface area of a sphere is 4πr²] An open hemisphere of radius 5.5 cm is used to make a metal kitchen strainer. 50 holes are cut out of the curved surface. Assume that the piece of metal removed to make each hole is a circle of radius 1.5 mm. Calculate the external surface area that remains.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.
- [2] M1 for 1/2 × 4/3 × π × r³ = 20 soi or SC1 for 1.68
- 2.12
- [2] B1 for (50/20)^(1/3) or (20/50)^(1/3) oe or M1 for (r2/r1)³ = 50/20 oe
- 6.79
- [3] M1 for π(figs 15)² oe and M1 for 1/2 × 4 × π × (figs 55)² – 50 × their πr²
- 187
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