Question

A cone is inscribed in a regular square pyramid. If the pyramid has a base edge of 6" and a slant height of 9", find the volume of the cone. 12√2 18√2 27

Answer 1

Check the picture below.

so, a cone inscribed in a square pyramid, like the blue one there, will have the a diameter that is the length of the base of the pyramid, as you can see there, is 6, now, since the radius is half of the diameter, that means r = 3.

we know the slant height is 9, since the slant height and the height segment make a right-triangle with the base's segment, then we use the pythagorean theorem to get the height "h".

$\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=radius\\ h=height\\ -----\\ r=3\\ h=6\sqrt{2} \end{cases} \implies V=\cfrac{\pi (3)^2(6\sqrt{2})}{3}$