WAEC - Mathematics (1995 - No. 27)
The diagram above shows a cone with the dimensions of its frustrum indicated. Calculate the height of the cone.
12cm
15cm
18cm
24cm
30cm
Explication
Considering the smaller and larger triangle, these two are similar triangles. Hence,
If the height of the smaller triangle = h,
\(\therefore \frac{h}{6} = \frac{h + 12}{12}\)
\(12h = 6h + 72 \implies 6h = 72\)
\(h = 12 cm\)
\(\therefore\) The height of the cone = 12 + 12 = 24 cm