Question

It is proposed to build a single circular park equal in area to the sum of areas of two circular park of diameter 16 m and 12 m in a locality. The radius of the new park would be 15 m.

• A. 10
• B. False

Answer 1

Answer: (B)

Area of first circular park whose diameter is 16 m.
= $\pi r^2$
= $\pi 8^2$ [radius = 8 m]
= 64$\pi$ $m^2$
Area of second circular park whose diameter is 12 m.
= $\pi r^2$
= $\pi 6^2$ [radius = 6 m]
= 36$\pi$ $m^2$
According to the given condition
Area of single circular park = Area of first circular park + Area of second circular park
$\pi R2=64\pi +36\pi$ [Let R be the radius of single circular park]
$\pi$ $R^2$ = 64 $\pi$ + 36 $\pi$
$R^2$ = 100
R = 10 m