Question

It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters $16m$ and $12m$ in a locality. The radius of the new park would be

• A. $10m$
• B. $15m$
• C. $20m$
• D. $24m$

Answer 1

Answer: (A)

$10m$

The radius of one park $r_1=\frac{1}{2}\times 16m=8m$

& that of another one $r_2=\frac{1}{2}\times 12m=6m.$

$\therefore$ The sum of their areas

$=\pi {r_1}^2+\pi {r_2}^2=\pi ({r_1}^2+{r_2}^2)=\pi (8^2+6^2)m^2=100\pi m^2.$

Again, let the radius of the proposed park be $r.$

$\therefore$ Its area $=\pi r^2.$

$\therefore$ By the given condition $\pi r^2=100\pi m\Rightarrow r=10m.$