JAMB 2000 · UME · Q24

Solid mensuration

A frustum of a pyramid with a square base has its upper and lower sections as squares of sides 2 m and 5 m respectively, and the distance between them is 6 m. Find the height of the pyramid from which the frustum was obtained.

Worked solution (try it first)

Let the full pyramid have height $H$ .
The small pyramid cut off the top has height $H - 6$ and base side 2 m.
Similar pyramids: side is proportional to height, so $\dfrac{2}{5} = \dfrac{H - 6}{H}$ .
Cross-multiply: $2H = 5H - 30$ , so $3H = 30$ and $H = 10$ m, option D.

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