O-LevelMathematicsMensuration4024/11 · Oct/Nov 2025 · Q177 Marks
The diagram shows a prism. [Figure 17.1] The cross-section of the prism is an isosceles triangle with sides 13 cm, 13 cm and base 10 cm. The length of the prism is 3 cm.
- (a)Show that the volume of the prism is 180 cm³.[4]
- (b)A mathematically similar prism has a volume of 1440 cm³. The cross-section of this prism is an isosceles triangle with base x cm. Calculate the value of x.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- [M2] (a) [height =] 12
- [M1] for h² + 5² = 13² oe or better
- [A2] (1/2)*10*sqrt(13^2-5^2) * 3 oe leading to 180
- [M1] for (1/2)*10*their(sqrt(13^2-5^2)) * 3
- [3] (b) 20
- [M2] for (10/x)^3 = 180/1440 oe or (x/10)^3 = 1440/180 oe or M1 for 180/1440 oe or (10/x) or (x/10) or ratio of lengths or ratio of volumes.
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