O-LevelMathematicsMensuration4024/21 · May/June 2015 · Q46 Marks
[Figure of cone/hemisphere] [The volume of a cone = (1/3)πr²h] [The volume of a sphere = (4/3)πr³] A solid is formed by joining a cone of radius 4.5 cm and height 7.6 cm to a hemisphere of radius 4.5 cm as shown.
- (a)Calculate the area of the circle where they are joined.[2]
- (b)Calculate the total volume of the solid.[2]
- (c)Another solid of the same type is made by joining a cone of radius 5 cm and height h cm to a hemisphere of radius 5 cm. The cone and hemisphere have equal volumes. Calculate the height of the cone.[2]
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 2015). The mark or mark type is shown in brackets.
- [2] 63.6 to 63.62; M1 for πr²
- [2] 352 to 353; B1 for 161(.2) or 190.9 or 191
- [2] 10; M1 for (1/3)π5²h or (2/3)π5³
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