Question

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 ft, and the entire length of the silo is 9.5 ft. Which of the following could be used to calculate the total volume of grains that can be stored in the silo? π(2ft)2(8ft) + one over threeπ(2ft)2(9.5ft − 8ft) π(8ft)2(2ft) + one over threeπ(2ft)2(9.5ft − 8ft) π(2ft)2(8ft) + one over threeπ(9.5ft − 8ft)2(2ft) π(8ft)2(2ft) + one over threeπ(9.5ft − 8ft)2(2ft)

Answer 1

The following that could be used to calculate the total volume of grains that can be stored in the silo is π(2 ft)²8 ft + 1/3π(2 ft)²(9.5 ft - 8ft)

To answer the question, we need to know what volume is.

What is volume?

This is the capacity of a material or container.

Since the silo is made of a cylindrical and a conical part, we need to find the volume of both parts.

Volume of cylindrical part.

So, the volume of the cylindrical part V = πr²h where

• r = radius of cylidrical part = 4 ft/2 = 2 ft and
• h = length of cylindrical part = 8 ft.

So, V = πr²h

V = π(2 ft)²8 ft

Volume of the conical part

The volume of the conical part is given by V' = 1/3πr²h where

• r = radius of cone = 2ft and
• h = height of cone.

Since the entire length of silo is 9.5 ft and length of cylindrical part is 8 ft, then the height of cone is h' = 9.5 ft - 8 ft

So, V' = 1/3πr²h'

V' = 1/3π(2 ft)²(9.5 ft - 8ft)

Total volume of grains in silo

The total volume of grains equals the total volume of the silo V" = V + V'

V" = π(2 ft)²8 ft + 1/3π(2 ft)²(9.5 ft - 8ft)

So, the following that could be used to calculate the total volume of grains that can be stored in the silo is π(2 ft)²8 ft + 1/3π(2 ft)²(9.5 ft - 8ft)

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