A grain silo is a cylinder with a hemisphere on top. In the Happy Farms grain silo, the height of the cylindrical portion is 30 feet. The radius is 10 feet. The volume of a cylinder is given by V = πr2h. 1. How can you find the volume of a hemisphere?

2. What is the volume of the hemisphere? Show your work.

3. What is the volume of the cylinder? Show your work.

4. What is the total volume of the grain silo? Explain how you found your answer.

1) The volume of a hemisphere of radius R is equal to half the volume of a sphere of radius R.

Where the volume of a sphere of radius R is:

V = (4/3)*pi*R^3

In this case, the radius is R = 10ft

And pi = 3.14

2) Now we can just solve that equation to get:

V = (1/2)*(4/3)*3.14*(10ft)^3 = 2,093.33 ft^3

Where the (1/2) comes because the volume of the hemisphere is half the volume of a complete sphere, as we already said above.

4) We know that the volume of a cylinder is:

V = pi*(r^2)*h

where:

pi = 3.14

r represents the radius. The radius of the cylinder will be the same as the radius of the hemisphere, then r = 10ft

h is the height of the cylinder, in this case, h = 30ft

Then the volume is:

V = 3.14*(10ft)^2*(30ft) = 9,420 ft^3

The total volume is equal to the sum between the volumes of the cylinder and the volume of the hemisphere.

Then the total volume is:

Volume =  9,420 ft^3 + 2,093.33 ft^3 = 11,513.33 ft^3