b Subtract the answer from Part A from the area of the square.
A
a π r^2 +18π r + 81π ≈ 3.14r^2 +56.52r + 254.34 ft^2
B
b -3.14r^2 -56.52r +1189.66 ft^2
Practice makes perfect
a To find the area of the large circle, we first need to write an expression for its radius. Since the radius of the large circle is 9 ft longer than the radius of the inner circle we can add 9 to the radius of the inner circle to get its radius, r+9.
If we approximate π ≈ 3.14, we get 3.14r^2 +56.52r + 254.34 ft^2.
b To find the area of the portion outside the outer circle, we need to subtract our answer from Part A from the area of the square. Let's find the area of the square.
Now. we can subtract the outer circle's area that we derived in Part A from 1444 ft^2.
1444-(3.14r^2 +56.52r + 254.34)
⇕
1444-3.14r^2 -56.52r - 254.34
When we combine like terms, we get -3.14r^2 -56.52r +1189.66 ft^2.
