Question

What radius of a circle is required to inscribe a square with an apothem of 4.95 inches?

a. 5in
b. 6in
c. 7in
d. 8in

Please explain how to get the answer, I want to know how to do this and not just be given the answer

Answer 1

we know that
The apothem goes from the center to mid-point in one of the square sides.
then
If the apothem is -------> 4.95 in
so
the length of one side of the square is 2 * 4.95--------> 9.9 in
the diameter of the circle is equals to the diagonal of the square

applying the Pythagorean theorem

a²+ b²= c²
a = b ---------> 9.9 in

2a² = c²
c²=2 * 9.9²
c²=196.02----------> c=√196.02---------- > c=14 in
the diameter is 14 in
so
the radius r=14/2----------> r=7 in

the answer is the option
c. 7 in