Question

It is proposed to build a single circular park whose area is equal to the sum of the areas of two circular parks of diameters $24\text{m}$ and $10\text{m}$ in a locality. The radius of the new park will be

• A. $8\text{m}$
• B. $13\text{m}$
• C. $15\text{m}$
• D. $16\text{m}$

Answer 1

The correct option is B $13\text{m}$

Let the radius of the new park be $r$.
Given that area of the circular park is equal to the sum of area of two circular parks of diameter $24\text{m}$ and $10\text{m}$.
$\Rightarrow \pi r^2=\pi {\left(\frac{24}{2}\right)}^2+\pi {\left(\frac{10}{2}\right)}^2$
$\Rightarrow r^2=(12{)}^2+(5{)}^2=144+25$
$\Rightarrow r=\sqrt{169}=13\text{cm}$
Hence, the correct answer is option b.