Questions: A circular pool measures 18 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 6 inches, how wide will the border be? (1 cubic yard = 27 cubic feet)

A circular pool measures 18 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 6 inches, how wide will the border be? (1 cubic yard = 27 cubic feet)

Transcript text: A circular pool measures 18 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 6 inches, how wide will the border be? (1 cubic yard = 27 cubic feet)

Solution

Solution Steps

Step 1: Convert all measurements to consistent units

Depth of the border in feet: 0.5 feet

Step 2: Calculate the radius of the pool

Radius of the pool, \(r_p\): 9 feet

Step 3: Calculate the volume of the border material in cubic feet

Volume of the border material, \(V\): 27 cubic feet

Step 4: Use the formula for the volume of a cylindrical shell to find the outer radius of the border

Outer radius of the border, \(r_b\): 9.909 feet

Step 5: Calculate the width of the border

Width of the border, \(W\): 0.91 feet

Final Answer: The uniform width of the circular border around the circular pool is {W_rounded} feet.

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