Question

If the radius of a circle is tripled, the area becomes:

• A. $9$ times
• B. $3$ times
• C. $6$ times
• D. $30$ times

Answer 1

The correct option is A

$9$ times

Explanation of correct option:

Determine the new area:

If the radius $r$ is tripled, the new radius is $3r$.

i.e., $r_n=3r$

As we know,

Area of circle $\left(A\right)={\mathrm{\pi r}}^2$

Let, the new area be $A\text{'}$.

Now, the New Area of the circle will be,

$$\begin{gathered} \Rightarrow A\text{'}=\mathrm{\pi }{\left(3\mathrm{r}\right)}^2 \\ \Rightarrow A\text{'}=9{\mathrm{\pi r}}^2 \\ \Rightarrow A\text{'}=9\times {\mathrm{\pi r}}^2 \\ \Rightarrow A\text{'}=9\times A\mathbf{}\mathbf{[}\mathbf{\because }\mathbf{}\mathbf{A}\mathbf{=}{\mathbf{\pi r}}^{\mathbf{2}}\mathbf{]} \end{gathered}$$

i.e., the new area $A\text{'}$ is $9$ times the old area $A$.

Hence, option A is the correct option.