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

Options

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

Answer

A

Explanation

Area of first circular park, whose diameter is 16m
= `pir^(2) = pi((16)/(2))^(2)= 64 pim^(2)` [`because r=(d)/(2)=(16)/(2)=8m`]
Area of second circular park, whose diameter is 12m
`pi((16)/(2))^(2)= 64 pim^(2)` [`because r=(d)/(2)=(16)/(2)=8m`]
According to the given condition,
Area of single circular park = Area of first circular park + Area of second circular park
`piR^(2)=64 pi +36pi` [`because` R be the radius of single circular park]
`rArr piR^(2)= 100pi rArr R^(2)= 100`
`:.` R = 10m