A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top (see the figure). The diameter of the silo is to be 30 feet, but the height is yet to be determined. Find the height h of the silo that will result in a capacity of 11,700π ft3.
Volume = 2/3 pi r^3 + pi r ^2 *h = pi (2/3 * r3 + hr2) 11700 pi = pi (2/3 * r3 + hr2) 11700 = 2/3 * r3 + hr2 r = 15 11700 = 2/3*15^3+h*15^2 11700 = 2250+225h 9450=225h h=42 It is 42 ft high.
The volume will be 2/3 pi r^3 + pi (r)^2 h You want this to total 11,700 pi and you know that r = 15 Factoring out the pi you need 2/3 (15)^3 + (15)^2 h = 11700 (2/3) 3375 + 225h = 11700 2250 + 225h = 11700 225h = 11700 - 2250 225h = 9450 h = 9450 /225 = 42
