Answer to Question #124942 in Geometry for Jonathan

Question

A grain silo is shown below:

Grain silo formed by cylinder with radius 6 feet and height 168 feet and a half sphere on the top

What is the volume of grain that could completely fill this silo, rounded to the nearest whole number? Use 22 over 7 for pi.

19,008 ft3

19,461 ft3

6,336 ft3

453 ft3

Answer 1

V=total volume, R=6ft, H=168ft.

V=V(cylinder)+1/2V(sphere)

V(cylinder)=$\pi$ *R²*H=(22/7)*36*168=19008ft³

1/2V(sphere)=(1/2)*(4/3)*$\pi$ *R³=(2/3)*(22/7)*216=452.571429ft³

V=19008+453=19461ft³