Question

GEOMETRY The area of the circle is$\mathbf{36}\mathbf{\pi }$ square units. If the radius is doubled, what is the area of the new circle?

$$\begin{gathered} \mathbf{F}\mathbf{}\mathbf{72}\mathbf{\pi }\mathbf{}{\mathbf{units}}^2 \\ \mathbf{G}\mathbf{}\mathbf{144}\mathbf{\pi }\mathbf{}{\mathbf{units}}^2 \\ \mathbf{H}\mathbf{}\mathbf{1296}\mathbf{\pi }\mathbf{}{\mathbf{units}}^2 \\ \mathbf{J}\mathbf{}\mathbf{9}\mathbf{\pi }\mathbf{}{\mathbf{units}}^2 \end{gathered}$$

Short answer

The area of a new circle is $\mathbf{144}\mathbf{\pi }{\mathbf{units}}^2$.

Step-by-step solution

Step 1. Write formula for area of circle.

The area of circle is given by $A=\pi r^2$.

Step 2. Substitute.

Substitute$36\pi$ for A in $A=\pi r^2$.

$\begin{array}{c}36\pi =\pi r^2\\ 36=r^2\\ 6=r\end{array}$

Therefore, the radius of the circle is 6 units.

Step 3. Find the area of new circle.

If the radius of circle is doubled, the new radius is 12 units. Therefore, area of a new circle is

$$\begin{gathered} A=\pi {\left(12\right)}^2 \\ =144\pi unit{s}^2 \end{gathered}$$

Therefore, option G is the required answer.