Question

Assume the lot you purchased is 100 ft by 160 ft. You are ready to design your playground. There are young children in the neighborhood, so you want to include a sandbox. You can use ¼ of the total playground for the sandbox. What is the maximum length and width of the sandbox? Assume that the height of the sandbox is 1.5 foot high. What is the volume of the sandbox? A fifty pound bag of play sand will fill approximately ½ of a cubic foot, and you wish to fill the sandbox ¾ high, how many bags of sand will you need to purchase?

Answer 1

Total area of the playground = 100 ft x 160 ft = 16,000 square feet

1/4 or .25 times this is how much area the sandbox can occupy.

.25 x 16,000 = 4,000 square feet

The length and width of the sandbox can be sqrt(4000) = 63.2 feet

The volume is the length x width x height = 63.2 x 63.2 x 1.5 = 5991.4 cubic feet

3/4 or .75 of the volume of the sandbox
.75 * 5991.4 = 4493.6 cubic feet

You need 2 times this amount in bags to fill the sandbox since each bag is 1/2 cubic foot.

4493.6 * 2 = 8988 bags of sand.