Question

Question 6
It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diamters 16 m and 12 m in a locality . The radius of the new park would be
(A) 10 m
(B) 15 m
(C) 20 m
(D) 24 m

Answer 1

Area of first circular park whose diameter is 16 m.

$=\pi r^2=\pi {\left(\frac{16}{2}\right)}^2=64\pi m^2[\because r=\frac{d}{2}=\frac{16}{2}=8m]$

Area of second circular park, whose diameter is 12 m

$=\pi {\left(\frac{12}{2}\right)}^2=\pi (6{)}^2=36\pi m^2[\because r=\frac{d}{2}=\frac{12}{2}=6m]$

According to the given condition,

Area of single circular park

= Area of first circular park + Area of second circular park

$=\pi r^2=64\pi +36\pi$

$[\because Rbetheradiusofsinglecircularpark]$

$\Rightarrow \pi R^2=100\pi \Rightarrow R^2=100$

$\therefore R=10m$