A silo is in the shape of a cylinder with a half sphere on top.
The volume is equal to: 1/2 * 4PIr^3/3 + h*PIr^2 (1/2 the volume of a sphere of radius r plus the cylindrical volume) where h is the height of the cylinder, not the silo. 1/2 * 4*7^3PI/3 + h*7^2PI = 5000 Multiply both sides by 3 and multiply terms out giving: 686PI + 147hPI = 15000 or 147PIh = 15000 - 686PI h = (15000 - 686PI)/147PI h = 27.813934 ft. You need to add another 7 ft for the 1/2 sphere on top.
Treat the half-sphere and the cylinder seperately. 1) Calculate the volume of the 1/2 sphere - Volume of a sphere = 4/3 x pi x radius cubed (pi = 3.1714) divide the result by 2 2) subtract that from the 5000, 3) use the result to calculate the height of the sphere - Volume = pi x raduis squared x height (pi = 3.1714) 4) add the just calculated height of the cylinder + the height of the 1/2 sphere (7 ft) to get the total height of the silo
what is the radius of the silo?
32'-6 volume = pi x radius squared x height height = volume / pi x radius squared
