Answer to Question #148924 in Geometry for solid mensuration

Question

2. A regular square pyramid has an altitude of 12 m and volume of 196 m3. Determine the slant height of the pyramid.

Answer 1

Consider a regular square pyramid

Let $a=$ the base edge, $h=$ the altitude, and $s=$ the slant height.

The volume $V$ of the frustum of a regular square pyramid is

$$V=\dfrac{1}{3}a^2h$$

Then

$$a=\sqrt{\dfrac{3V}{h}}=\sqrt{\dfrac{3(196)}{12}}=7 (m)$$

By the Pythagorean Theorem from the right triangle

$$s^2=(\dfrac{a}{2})^2+h^2$$

$$s=\sqrt{(\dfrac{a}{2})^2+h^2}=\sqrt{(\dfrac{7}{2})^2+(12)^2}=12.5(m)$$

12.5 m