A silo is formed from a right circular cylinder and a right circular cone. The height of the cylinder is 6ft and the overall height of the silo is 10ft. The silo has a capacity of 144 cubic feet. What is the diameter of the silo?
try using the formula: (7*pi*(diameter)^2*height of the silo) divide by 24
You are given the volume, the height of the cylinder, and the overall height. Remember the volume of a cone is: 1/3 x Hcone x Pi x r^2 and the volume of a cylinder is: Hcylider x Pi x r^2. First we have to figure out the height of the cone. We know the overall height, and the height of the cylinder. Hsilo = Hcylinde + Hcone. 10 ft = 6 ft + Hcone. Hcone = 4 ft Now we can find the diameter of the silo. Assuming the diameter(and radius) of both the cone and the cylinder are the same V = 1/3 x Hcone x Pi x r^2 + Hcylider x Pi x r^2 Plugging in all of the known values gives us: 144 ft^3 = 1/3 x 4ft x Pi x r^2 +4 ft x Pi x r^2 144 ft^3 = 4/3 x Pi x r^2 +4 ft x Pi x r^2 144 ft^3 = 16.755 x r^2 Solving for r we have r = 2.93 ft So the diameter is two times r or: D = 5.86 ft - I hope this helps!
