# Help with my Solid Mensuration Problem

• Aug 21st 2013, 06:38 PM
PhillipMasagca
Prismatoids (Solid Geometry) Need Help for this Problem
Bunker Hill Monument is a stone structure in the form of the frustum of a regular square pyramid whose height is 220ft. and whose base edges are 15ft. and 30ft., respectively. Through the center of the monument is a cylindrical opening 11ft. in diameter at the top and 15ft. in diameter at the bottom. Find the volume of the stone in the monument.

The Answer in the back of the book Solid Mensuration by Kern and Bland is 86,068 cubic feet.
• Aug 21st 2013, 06:53 PM
MarkFL
Re: Help with my Solid Mensuration Problem
The formula for the volume of a truncated square pyramid is:

$\displaystyle V=\frac{h}{3}\left(a^2+ab+b^2 \right)$

where $\displaystyle h$ is the height, $\displaystyle a$ is the side length of the square base and $\displaystyle b$ is the side length of the square top.

The formula for a truncated cone is:

$\displaystyle \frac{h\pi}{3}\left(R_1^2+R_1R_2+R_2^2 \right)$

where $\displaystyle h$ is the height, $\displaystyle R_1$ is the radius of the base and $\displaystyle R_2$ is the radius of the top.

Can you proceed?
• Aug 21st 2013, 06:57 PM
PhillipMasagca
Re: Help with my Solid Mensuration Problem
Wait, I think i can't proceed it's because there is no given b (the square top) only the base is given with 15ft. and 30ft.
• Aug 21st 2013, 07:07 PM
MarkFL
Re: Help with my Solid Mensuration Problem
The base sides are 30 ft. and the top are 15 ft.