Question

A family is building a circular fountain in the backyard. The yard is rectangular and measures 7x by 6x and the fountain is going to be circular with a radius of 2x. Once the fountain is built, what will be the area of the remaining yard?
Can someone please walk me through this to help me understand? Thanks :)

Answer 1

yard area = 42 x^2
fountain area = pi r^2 = pi (4x^2)

so remaining area = (42 - 4pi)x^2

Answer 2

Hm well I know the right answer but I need to know how to get there. It says the answer is 2x^2(21-2pi)

Answer 3

see
[(42(x^2)-4pi(x^2)]
21*2(x^2)=42(x^2) rit?
2*2(x^2)pi=4(x^2)pi rit?
[(21*(2x^2)-(2x^2)*2pi)]
bring (2x^2) out
you get
(2x^2)(21-2pi)
do you undestand now