Chapter 2.6, Problem 10AYU

10. A circle of radius r is inscribed in a square. see the figure.

(a) Express the area A of the square as a function of the radius r of the circle.

(b) Express the perimeter p of the square as a function of r.

To determine

To find:

a. To express the area $A$ of the square as a function of the radius $r$ of the circle.

Answer to Problem 10AYU

Solution:

a. $A=4r^2$

Explanation of Solution

Given:

A circle of radius $r$ is inscribed in the square.

Calculation:

a. To express the area $A$ of the square as a function of the radius $r$ of the circle:

From the given figure, the side of the square$=2r$.

Therefore, Area of the square $=A=2r.2r=4r^2$.

To determine

To find:

b. To express the perimeter $p$ of the square as a function of $r$.

Answer to Problem 10AYU

Solution:

b. $p=8r$

Explanation of Solution

Given:

A circle of radius $r$ is inscribed in the square.

Calculation:

b. To express the perimeter p of the of the square as a function of $r$:

From the given figure, the side of the square $=2r$.

Therefore, Perimeter of the square $p=4\left(2r\right)=8r$.