Question

Area of a rectangle and the area of a circle are equal. If the dimensions of the rectangle are $14cm\times 11cm$, then radius of the circle is

• A. $21cm$
• B. $10.5cm$
• C. $14cm$
• D. $7cm$

Answer 1

The correct option is D

$7cm$

Correct option : (d) $7cm$

We know that,

Area of rectangle $=length\times breadth$

Area of circle $={\mathrm{\pi r}}^2$

Given, $length=14cm,breadth=11cm$

We have given that,

Area of rectangle $=$Area of circle

$$\begin{gathered} \Rightarrow length\times bredth={\mathrm{\pi r}}^2 \\ \Rightarrow 14\times 11=\frac{22}{7}\times {\mathrm{r}}^2 \\ \Rightarrow 154=\frac{22}{7}\times {\mathrm{r}}^2 \\ \Rightarrow {\mathrm{r}}^2=\frac{7}{22}\times 154 \\ \Rightarrow {\mathrm{r}}^2=49 \\ \Rightarrow \mathrm{r}=\sqrt{49} \\ \Rightarrow \mathrm{r}=7\mathrm{cm} \end{gathered}$$

Thus, the radius is $7cm$

Hence, the correct option is (d)