Mathematics · Oct / Nov 2022 · Paper 22 · Question 21
0580
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NOT TO SCALE 5.5 cm 9.2 cm 12.5 cm A solid is made by cutting a small cone from a larger cone, as shown in the diagram. The height of the larger cone is 12.5 cm. The height of the solid is 5.5 cm. The diameter of the base of the larger cone is 9.2 cm. Work out the volume of the solid. [The volume, V, of a cone with radius r and height h is r V r h 3 1 2 = .] cm3 [4] Questions 22 and 23 are printed on the next page.
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228 or 228.3 to 228.4 [4]
2 1 9.2
M1 for ×× π × 12.5 oe 3 2
M1 for 9.2 diameter oe or better = − 12.5 12.5 5.5 2 1 their 5.152 ×× × ( − )
M1 for π 12.5 5.5 3 2 oe OR
M2 for 2 π 9.2 π ( ) × × 12.5 − × r 2 × 12.5 − 5.5 oe 3 2 3 for any r < 4.6 If 0 scored
SC1 for 913 or 913.3 to 913.5
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