O-LevelMathematicsMensuration4024/22 · May/June 2025 · Q2111 Marks
The diagram shows a solid formed by joining a cone to a hemisphere. The diameter of the cone is 14 cm and the diameter of the hemisphere is 14cm. The total height of the solid is 24 cm. [Figure showing a cone on top of a hemisphere, with diameter 14cm and total height 24cm]
- (a)Calculate the volume of the solid.[3]
- (b)Show that the total surface area of the solid is 712 cm², correct to the nearest integer.[5]
- (c)A smaller solid is mathematically similar to this solid. The total surface area of the smaller solid is 242 cm². Calculate the total height of the smaller solid.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [3] M1 for 1/3 × π× 7³ oe M1 for 1/3 × π× 7² ×(24-7) oe
- [5] M2 for π×7×√( (24-7)²+7²) oe or M1 for (24-7)²+7² oe M1 for 1/2 ×4×π×7² oe A1 712.07 to 712.3
- [3] M2 for √(242/712) × 24 oe or 24 ÷ √(712/242) oe or M1 for [k]√(242/712) oe or [k]√(242/712) oe or 24²/h² = 712/242 or better
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