Question

A family is building a circular fountain in the backyard. The yard is rectangular and measures 10x by 15 and the fountain is going to be circular with a radius of 4x. Once the fountain is built, what will be the area of the remaining yard?

A.) 2x^2 (75-8
`\pi`)
B.) 150x^2-4
`\pi` x^2
C.) 134
`\pi` x^2
D.) 134x^2

Answer 1

the correct question is
A family is building a circular fountain in the backyard. The yard is rectangular and measures 10x by 15x and the fountain is going to be circular with a radius of 4x. Once the fountain is built, what will be the area of the remaining yard?

Step 1
find the area of rectangular yard (A1)
A1=(10*x)*15*x=150*x² units²

Step 2
find the area of the circular fountain (A2)
A2=pi*r²---------> pi*(4x)²=16*pi*x²

Step 3
find the area of the remaining yard (A3)

A3=A1-A2----------> 150*x²-16*pi*x²----> x²*[150-16*pi]----> 2*x²*[75-8*pi]

the answer is the option A)
2x² (75-8pi )