Question

A family is having a pool built in their backyard. Their yard is rectangular and measures 14x by 19x and the pool is circular with a radius of 6x. How much of the yard will be left over after the pool is built?
$A: 230 \pi x^{2} B: 230 x^{2} C: 266 x^{2} -6 \pi x^{2} D:2 x^{2} (133-18 \pi )$

Answer 1

You want to find the area left over after the pool is built, so subtract the area of the pool from the area of the yard.

Area of Yard= Base x Height = 14x*19x = 266x^2
Area of Circle= Pi x Radius^2 = (6x)^2*pi = 36x^2*pi

Now subtract the two areas:
266x^2-(36^2*pi)
266x^2-36x^2*pi

Take 2x^2 as a common factor:
2x^2(133-18pi)

D: 2x^2(133-18pi)

Hope this helps :)