A family is having a pool built in their backyard. If their backyard is rectangular and measures 8x by 7x and the pool is circular with a radius of 3x how much of the yard will be left over after the pool is built?
First, let's find the area of the backyard:
Area = length x width
Area = 8x x 7x
Area = 56x^2
Next, let's find the area of the pool:
Area of a circle = π x radius^2
Area of pool = π x (3x)^2
Area of pool = π x 9x^2
Area of pool = 9πx^2
Now, let's find the area of the yard that will be left over after the pool is built:
Area left over = Area of backyard - Area of pool
Area left over = 56x^2 - 9πx^2
Approximating the value of π to 3.14, we get:
Area left over = 56x^2 - 9(3.14)x^2
Area left over = 56x^2 - 28.26x^2
Area left over = 27.74x^2
Therefore, approximately 27.74x^2 of the yard will be left over after the pool is built.