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andriy [413]
4 years ago
13

A family is building a circular fountain in the backyard. The yard is rectangular and measures 10x by 15 and the fountain is goi

ng 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
Mathematics
1 answer:
Ira Lisetskai [31]4 years ago
3 0
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 <span>fountain (A2)
A2=pi*r</span>²---------> pi*(4x)²=16*pi*x²

Step 3
find <span> the area of the remaining yard (A3)

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

the answer is the option A) 
<span> 2x</span>²<span> (75-8pi )</span>

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