Here is the problem:A Farmer's silo is in the shape of a cylinder with a hemisphere as the roof. If the height of the silo is 117 feet and the radius of the hemisphere is r feet, express the volume of the silo as a function of r. Any help would be greatly appreciated!
Hi, Volume of cylinder = (pi)*(height)*(radius of base)^2 Volume of hemisphere = (2/3)*(pi)*(radius)^3 Volume of Silo = Volume of cylinder + Volume of hemisphere Lets do the cylinder first: Cylinder height : 117 Cylinder base radius : r (same as hemisphere's radius) Thus: Volume of cylinder = (pi)*(height)*(radius of base)^2 = (pi)*(117)*(r)^2 Now for the hemisphere: Hemisphere radius : r Thus: Volume of hemisphere = (2/3)*(pi)*(radius)^3 = (2/3)*(pi)*(r)^3 So then for the Silo: Volume of Silo = Volume of cylinder + Volume of hemisphere = (pi)*(117)*(r)^2 + (2/3)*(pi)*(r)^3 = (pi)*(r)^2*( 117 + (2/3)*r ) Volume of Silo = (pi)*(r)^2*( 117 + (2/3)*r )
