A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attaced to the top. The diameter of the silo is to be 30 feet, but the height is yet to be determined. Find the height h of the sil that will result in a capacity of 11,250pi ft^3.
(4/6) PI r^3 + PI r^2 h = 11,250 (4/6) pi (15)^3 +pi (15)^2 h =11,250 solve for h Volume of a hemisphere is (4/6) PI r^3 pi=3.14 7065+706.5h=11,250 706.5h =4185 h=5.92 ft
The silo is two volumes... the hemisphere and the cylinder. The approach is to calculate the volume of the hemisphere, which does not depend on height, subtract that from the total required and then divide the resulting volume of the cylinder by its ground area. Remembering you are asked for the height of the total silo, finally add the height of the hemisphere to the height of the cylinder Volume of sphere is 4/3 * pi *r^3 Volume of hemisphere is 2/3 * pi *r^3 = 2/3 * pi * 15^3 =7068.6 cu.ft. So volume of cylinder is 11250 - 7068.6 = 4181.4 cu.ft. Height of cylinder = 4181.4/area = 4181/(pi * r^2) = 4181/(pi * 15^2) = 5.92 ft. The height of the hemisphere is its radius so: So the total height is 5.92 + 15 = 21 ft. to the nearest foot.
r=30/2=15 v=pi*r^2*h=11250 15^2*pi*h=11250 h=11250/625pi
