Question

The Volume of a pyramid with a square base is 200 cubic cm. The height of the pyramid is 13cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?

Accepted Answer

C. Volume $V = \frac{1}{3} a^2 h = 200 \implies \frac{1}{3} a^2 (13) = 200 \implies a^2 = \frac{600}{13}$. Distance from center of base to a vertex $d = \frac{a}{\sqrt{2}}$. So $d^2 = \frac{a^2}{2} = \frac{300}{13}$. Slant edge $e = \sqrt{h^2 + d^2} = \sqrt{13^2 + \frac{300}{13}} = \sqrt{169 + 23.0769} = \sqrt{192.0769} \approx 13.86 	ext{ cm}$. Rounded to nearest integer, $e = 14$ cm.

Slant Edge of Square Pyramid

Explanation

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