A family is having a pool built in their backyard. If their yard is rectangular and measures 10x by 10x and the pool is circular with a radius of 2x how much of the yard will be left over after the pool is built? Write your answer in factored form.

area of rectangle=legnth times width
area of circle=pi time radius^2

are left=yard-pool

given
legnth an dwidth are 10x
area=10x times 10x=100x^2=yard

area of pool=
pi times (2x)^2
pi times 4x^2
4pix^2=pool

yard-pool=100x^2-4pix^2=(100-4pi)x^2
aprox
87.42x^2 of the yard

minus

Answer Link

MrRoyal MrRoyal · Answer 2 · 2022-04-20T07:20:47-04:00

4x²(25 - π) of the yard will be left over after the pool is built

How to determine the area?

The given parameters are:

Dimension of rectangular yard is 10x by 10x
The radius of the pool is 2x

The area of the rectangular yard is calculated as:

Yard = 10x * 10x

Evaluate

Yard = 100x²

The area of the pool is:

Pool = πr²

So, we have:

Pool = π(2x)²

Evaluate

Pool = 4πx²

Calculate the difference (d)

d = 100x² - 4πx²

Factor out 4x²

d = 4x²(25 - π)

Hence, 4x²(25 - π) of the yard will be left over after the pool is built