A company that manufactures storage bins for grains made a drawing of a silo. The silo has a conical base, as shown below:

The figure shows a silo shaped as a closed cylinder with a conical end. The diameter of the silo is 4 ft, the length of the cylindrical part is 8.5 ft, and the entire length of the silo is 13 ft.

Which of the following could be used to calculate the total volume of grains that can be stored in the silo?

π(8.5ft)2(2ft) + one over threeπ(2ft)2(13ft − 8.5ft)
π(2ft)2(8.5ft) + one over threeπ(2ft)2(13ft − 8.5ft)
π(8.5ft)2(2ft) + one over threeπ(13ft − 8.5ft)2(2ft)
π(2ft)2(8.5ft) + one over threeπ(13ft − 8.5ft)2(2ft)

The volume of the silo is (π×2²×8.5+ ×π×2²×(13-8.5)) cube ft.

Step-by-step explanation:

Given,

The silo consists of a cylinder and a cone.

The diameter of the silo = 4 ft

The length of the cylindrical part = 8.5 ft

The entire length of the silo = 13 ft.

To find the volume of the silo.

The volume of the silo = the volume of cylinder + the volume of the cone

Formula

r be the radius and h be the height

Now,

The radius of the cylinder = 2 ft.

Height = 8.5 ft

Volume = π×2²×8.5 cube ft

Again,

The radius of the cone = 2 ft

Height = 13-8.5 = 4.5 ft

Volume =  ×π×2²×4.5 cube ft

Hence,

The volume of the silo = (π×2²×8.5+ ×π×2²×(13-8.5)) cube ft.

The correct option is B.

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