O-LevelMathematicsMensuration4024/22 · Oct/Nov 2020 · Q49 Marks

(a) [Volume of a sphere = 4/3 πr³] [Surface area of a sphere = 4πr²] [Figure 4.1] The diagram shows a solid formed by joining a cylinder to a hemisphere. The diameter of the cylinder is 9 cm and its height is 16 cm.

(a)(i)The volume of the hemisphere is equal to the volume of the cylinder. Show that the radius of the hemisphere is 7.86 cm, correct to 2 decimal places.[4]
(a)(ii)Calculate the total surface area of the solid.[3]
(b)A different solid is in the shape of a cuboid. The cuboid measures 8 cm by 4 cm by 6 cm. These measurements are given correct to the nearest centimetre. Calculate the lower bound of the volume of the cuboid.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[4] M2 for setting volumes equal: 1/2 * (4/3)πr^3 = π(9/2)^2 * 16 (oe); (M1 for correct volume of hemisphere oe; M1 for correct volume of cylinder oe); A1 for r = 7.862...; Show that r = 7.86 cm (2 d.p.).
[3] M1 for curved surface area of cylinder (π × 9 × 16 oe); M1 for total surface area of hemisphere (3 × π × 7.86² oe); Final answer 1030 or 1040 or 1034.6 to 1035.1.
[2] M1 for 7.5 × 3.5 × 5.5; Final answer 144.375.

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