O-LevelMathematicsMensuration4024/22 · May/June 2021 · Q97 Marks
[Volume of a cone = 1/3 πr²h] [Curved surface area of a cone = πrl] A cone has radius 6 cm and slant height l cm. The total surface area of the cone is 84π cm².
- (a)Show that l = 8.[2]
- (b)Calculate the volume of the cone.[3]
- (c)A similar cone has a total surface area of 47.25π cm². Find the radius of this cone.[2]
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Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [2] (a) 6πl + π×6^2 OR 84π - π× 6^2 M1 6πl + π×6^2 = 84π leading to l = 8 OR 6πl = 84π - π×6^2 leading to l = 8 A1 A0 if any errors or omissions
- [3] (b) 199 or 200 or 199.4 to 199.5... M2 for 1/3 π×6^2×√8^2-6^2 or M1 for 8^2 – 6^2 or 1/3 π×6^2×their h
- [2] (c) 4.5 nfww B1 for √47.25π/84π soi or √84π/47.25π soi or M1 for a correct equation in r
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