O-LevelMathematicsMensuration4024/21 · May/June 2022 · Q410 Marks
(a) A cuboid has dimensions x cm by x cm by 10 cm. The volume of the cuboid is 62.5 cm³. Find the value of x. (b) [Figure showing a sector AOB] A piece of card, AOB, is a sector of a circle, centre O, with angle 84° and radius 15 cm.
- (a)A cuboid has dimensions x cm by x cm by 10 cm. The volume of the cuboid is 62.5 cm³. Find the value of x.[2]
- (b)(i)Show that the arc length of the sector is 7π cm.[1]
- (b)(ii)OA is joined to OB to form the curved surface of a cone. Calculate the radius of the cone.[2]
- (b)(iii)Find the height of the cone.[2]
- (c)An empty barrel, in the shape of a cylinder, has radius 20 cm and height 80 cm. The barrel is filled with water at a rate of 5500 cm³/minute. Calculate the time taken to completely fill the barrel. Give your answer in minutes and seconds, correct to the nearest second.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [2] 2.5 or 2 1/2
- M1 for x × x × 10 = 62.5 oe
- [1] 84/360 × π × 2 × 15 leading to 7π or 84/180 × π × 15 leading to 7π
- [2] 3.5 or 3 1/2
- M1 for 2 × π × r = 7π oe or 84/360 × π × 15² = π × r × 15 oe
- [2] 14.6 or 14.58 to 14.59
- M1 for 15² – (their3.5)² oe
- [3] 18 [minutes] 17 [seconds] cao
- M2 for (π × 20² × 80) / 5500
- or M1 for π × 20² × 80 or theirvolume / 5500
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