Question

The largest possible circle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square feet, of the remaining board?

5 FT 2 squared
10 Ft 2 squared
15 Ft 2 squared
20 Ft 2 Squared

Answer 1

20ft ^2 (squared)

Explanation:

We deduct the circle area from the square area but first find out the radius triangle segment the 1/diagonal of the square. To find the hypotenuse h= c=r

h^2 =c = a+ b

h^2 = 8^2+ 8^2

h^2 =√64 + √64

h^2 =√128 = 11.313708499/3 = 3.77123616633

r= 5.65ft or 5.66ft rounded up

Square area formula = L x W = 8ft x 8ft = 64ft^2

Circle area formula= A=πr2 = (π = 3.14159265359 (3.77123616633x 3.77123616633) = 14.2222222222 x 3.14159265359 = 44.680428851

A = 14.2 x π

A = 44.68ft

64 - 44.68 = 19.32ft^2

The answer must be 20ft ^2 squared.