Question

A family is having a pool built in their backyard. If their yard is rectangular and measures 10x by 5x 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.
Any help would be greatly appreciated I can't figure out how to work this out

Answer 1

So, we know we have a rectangular yard with sides of \(10x\) and \(5x\). Inside that yard we have a circular pool with radius of \(2x\) and we're asked how much of the yard is not taken by the pool.
So let's calculate the areas of the yard and the pool first:
$$
\text{pool_area} = \pi r^2 = \pi (2x)^2 = \pi 4 x^2 \\
\text{yard_area} = (10x) \cdot (5x) = 50x^2
$$So first, let's calculate the area in the yard NOT taken by the pool. that would be:
$$
\text{not_pool_area} = \text{yard_area} - \text{pool_area} = \\
= 50 x^2 - \pi 4 x^2 = x^2(50 - 4\pi) = 2x^2(25 - 2\pi)
$$
Compare to this:
https://answers.yahoo.com/question/index?qid=20111229183114AAtB9pG
And figure out which form you need.

Hope it helps =)

Answer 2

Wow! Thank you!!

Answer 3

You're welcome \( \Large ☺\)