   SEARCH HOME Math Central Quandaries & 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.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.