A circle with diameter of 14 inches lies inside a square. What is, to the nearest tenth, the area of the region t is inside the square and outside the circle?

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Answer 1 · 2017-10-23T19:01:18

See a solution process below:

Because the circle lines within the square, the diameter of the circle is all the length of a side of the square.

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The formula for the area of a square is: #A_s = s^2#

We can substitute #14"in"# for the #s# giving:

#A_s = (14"in")^2#

#A_s = 196"in"^2#

The formula for the area of a circle is: #A_c = pir^2#

#r# is #1/2# the diameter of #7"in"# in this problem.

We can use #3.14159# for #pi# in this problem as the answer requests to the nearest 10th.

Substituting into the formula gives:

#A_c = 3.14159 xx (7"in")^2#

#A_c = 3.14159 xx 49"in"^2#

#A_c = 153.9"in"^2# rounded to the nearest tenth

The formula for calculating #t# is: #t = A_s - A_c#

Substituting the results from above gives:

#t = 196"in"^2 - 153.9"in"^2#

#t = 42.1"in"^2#