Mathematics · May / June 2026 · Paper 43 · Question 21
0580
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The question as text
0580/43/M/J/26 © Cambridge University Press & Assessment 2026 21 9 cm 8 cm 12 cm NOT TO SCALE The diagram shows a frustum. Calculate the volume of the frustum. cm3 [5]
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Show the answer and mark scheme
2870 or 2865 to 2866 nfww [18]
912π final answer for 5 marks 5
M4 for 1 3 π × 122 × 27 – 1
M4 for e.g. 1 3 π × 82 × 18 oe 3 × 9 × (π.82 + π.122 + π.8 .π.12 ) oe 2 2 3 For all marks accept volume scale factor 2 or for 1 3 π × 122 × 27 × (1 – ) oe unsimplified, e.g. 8 3 12 .
or M3 for 1 3 π × 122 × 27 oe Large cone: 1296π (but not from πr 2h = π × 122 × 9) or 1 3 π × 82 × 18 oe Small cone: 384π For B2 accept scale factors as ratios, e.g. 33 : 23.
or B2 for [height of cone] 27 or 18 nfww 3 3 2 3 or or oe Accept 0.667 or 0.6666... or better 3 2 For B1 accept scale factors as ratios, e.g. 12 : 8. h + h 9 =
or M1 for oe 8 12
or B1 for scale factor 2 3 or 3 2 or 1.5 soi i.e. heights differ by 9 If 0 scored,
SC1 for 1 3 π × 122 × (their h + 9) – 1 3 π × 82 × their h oe
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