The Surface area

Question

The top of the silo is a hemisphere with a radius of 12 ft. The bottom of the silo is a cylinder with a height of 40 ft. How many cubic feet of grain can the silo hold?

Use 3.14 for pi.

Enter your answer in the box. Round only your final answer to the nearest cubic foot.

Answer 1

Volume of a sphere is: V_S = 4/3πr³, where r is the radius of the sphere

Volume of a cylinder is: V_C = πr²h, where r is the radius and h is the height of the cylinder

Volume of the top is a hemisphere (half the sphere)

V_T = (1/2)(4/3)πr³

V_T = (2/3)π(12)³

V_T = 1,152π

The cylindrical bottom has a height of 40 ft. (h = 40), a radius of 12 ft. and a volume of:

V_B = πr²h

V_B = π(12)²(40)

V_B = 5,760π

The total volume is:

V = V_T + V_B

V = 1,152π + 5,760π

V = 6,912π

Using 3.14 for π:

V = 6,912(3.14)

V = 21,703.68

V = 21,704 cu. ft.