A circle is inscribed in a square with perimeter of 32 inches. What is the circumference of the circle, in inches? Express your answer in terms of pi.

Question

asked Jul 3, 2019 31.3k views

1 Answer

Soda · Answer 1 · 2019-07-10T11:39:39+0000

Since, a circle is inscribed in a square, it means that the side of a square is equal to the diameter of a circle.

Since, the perimeter of a square is 32 inches.

A perimeter is a path that surrounds the two dimensional shape.

Perimeter of square is given by

32 = 4 * side

side
= (32)/(4)

side = 8 inches.

Since, side of a square = diameter of a circle

Therefore, diameter of a circle = 8 inches.

radius of a circle =
(d)/(2) , where d is the diameter

radius =
(8)/(2) = 4 inches.

The perimeter of a circle is termed as Circumference.

Circumference of a circle =
$2\Pi r$

=
$2\Pi * 4$

=
$8\Pi$ inches.