#4 pre-calculus: find radius of grain silo

[greenblunts]

A grain silo consists of a cylindrical main section and a hemispherical roof. If the total volume of the silo (including the part inside the roof section) is 15000 ft{}^3 and the cylindrical part is 30 ft tall, what is the radius of the silo?

the vocabulary is losing me... grain silo?

 

[galactus]

You don't know what a silo is?. You must really be a city dweller .

A silo is a large round structure you see on farms which hold grain, silage, etc. Tall, cylindrical with a dome(hemisphere) on top.

Anyway, the volume for a cylinder is \(\displaystyle {\pi}r^{2}h\)

Volume of a hemisphere is 1/2 volume of a sphere, so \(\displaystyle \frac{2}{3}{\pi}r^{3}\)

Your equation is:

\(\displaystyle \L\\{\pi}r^{2}(30)+\frac{2}{3}{\pi}r^{3}=15000\)

Multiply by \(\displaystyle \frac{3}{\pi}\)

\(\displaystyle \L\\\frac{3}{\sout{\pi}}\sout{\pi}r^{2}(30)+\frac{\sout{3}}{\sout{\pi}}\frac{2\sout{\pi}}{\sout{3}}r^{3}=\frac{45000}{\pi}\)

\(\displaystyle \L\\2r^{3}+90r^{2}-\frac{45000}{\pi}=0\)
Solve for r.

 

[skeeter]

 

[galactus]

Wow, that's one of them "old-timey" silos. "They don't build 'em like that no more".