Geometry

Solids

Hard

A pyramid rises 'h' cm from a square base of side 'a' cm to a ridge parallel to one of the base's sides, and is the same length too. What is 'h' if the volume of the pyramid is half of that of a cube of side 'a'?

none of these

$\sqrt{3a}/2$

a/2

✅ Correct Option: 3

The solid is a wedge: square base $a\times a$ , top a ridge of length $a$ at height $h$ . By the prismatoid rule, $V=\frac{h}{6}(A_{bottom}+4A_{mid}+A_{top})=\frac{h}{6}(a^2+4\cdot\frac{a^2}{2}+0)=\frac{ha^2}{2}$ . Setting equal to $\frac{a^3}{2}$ gives $h=a$ .

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Solution

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