Question

A farmer plans to build the small silo shown to store chicken feed. What is the circumference of the base of the silo if it can hold a maximum of 132 cubic feet of feed?

Answer 1

Answer:

  4√(3π) ft ≈ 12.28 ft

Step-by-step explanation:

The formulas for volume of a cone and a cylinder can be used to find the radius of the silo. Then the formula for the circumference of a circle can be used to find the circumference.

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Relevant formulas are ...

• V = πr²h . . . . . volume, cylinder with radius r, height h
• V = 1/3πr²h . . . . volume, cone with radius r, height h
• C = 2πr . . . . . . . . circumference of a circle with radius r

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radius from volume

The total volume of the silo is the sum of the volumes of a cylinder of height (15 -6) = 9 ft, and a cone of height 6 ft. Both have the same radius: r. The total volume is given as 132 ft³.

  V = πr²h + 1/3πr²h' . . . . . . h = cylinder height, h' = cone height

  132 ft³ =  πr²(9 ft +1/3(6 ft)) = πr²(11 ft)

  r² = 132 ft³/(11π ft) = 12/π ft²

  r = √(12/π) ft = 2√(3/π) ft

circumference from radius

Then the circumference of the silo is ...

  C = 2πr = 2π(2√(3/π)) ft = 4√(3π) ft ≈ 12.28 ft

The circumference of the base of the silo is 4√(3π), about 12.28 feet.