12 In this question all lengths are in centimetres. 12
Р
h
B
8
The diagram shows a right triangular prism of height h inside a right pyramid.
The pyramid has a height of 12 and a base that is an equilateral triangle, ABC, of side 8.
The base of the prism sits on the base of the pyramid.
Points P, Q and R lie on the edges OA, OB and OC, respectively, of the pyramid OABC.
Pyramids OABC and OPQR are similar.
(a) Show that the volume, V, of the triangular prism is given by v = (ak? + bhP+ch) where a,
V3
b and c are integers to be found.
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