Math CentralQuandaries & Queries


Question from Calvin, a student:

A pool in the shape of a circle measures 10 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 3 inches, how wide will the border be? ( 1 cubic yard=27 cubic feet )

Hi Calvin.

The area of the ring (annulus is the mathematical term) which is your border times the depth of 3 inches equals the volume of concrete (27 cubic feet). Thus, we can divide the volume by the depth to find the area: 27 ÷ (3/12) = 108 square feet.

The area of the ring is the area of the outside circle of the border minus the area of the inside circle of the pool. Use A = πr² to calculate the area of the pool and then add 108 square feet. This should be the area of the outside border.

With this value, you can use A = πr² again and solve for the radius r. This, minus the 5 ft radius of the pool, is the width of the border.

Hope this helps,
Stephen La Rocque.

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