Chapter 12.2, Problem 9MRE

(a)

To determine

To find: The area of the circle.

Answer to Problem 9MRE

The area of the circle is $144\pi {\text{mm}}^2$ .

Explanation of Solution

Given information: It is given that the circle is inscribed in a square with sides $24\text{mm}$ .

Calculation:

Draw a diagram of a circle inscribed in a square.

  

Consider the side of the square as the diameter of the circle. The radius of the circle can be calculated as:

  $\begin{array}{c}r=\frac{d}{2}\\ =\frac{24\text{mm}}{2}\\ =12\text{mm}\end{array}$

The area of the circle with radius $r$ is given by,

  $A=\pi r^2$

Substitute $12$ for $r$ in the above formula.

  $\begin{array}{c}A=\pi {\left(12\text{mm}\right)}^2\\ =144\pi {\text{mm}}^2\end{array}$

Therefore, the area of the circle is $144\pi {\text{mm}}^2$ .

(b)

To determine

To find: The area of the square.

Answer to Problem 9MRE

The area of the square is $576{\text{mm}}^2$ .

Explanation of Solution

Given information: It is given that the circle is inscribed in a square with sides $24\text{mm}$ .

Calculation:

The area of the square is given by,

  $\text{Area}=a^2$

Substitute $24$ for $a$ in the above formula.

  $\begin{array}{c}\text{Area}={\left(24\text{mm}\right)}^2\\ =576{\text{mm}}^2\end{array}$

Therefore, the area of the square is $576{\text{mm}}^2$ .