SOLUTION: It 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

Algebra ->  Circles -> SOLUTION: It 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      Log On


   

Question 239337: It 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
(A) 10 m (B) 15 m (C) 20 m (D) 24 m
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
The two smaller parks have diameters of 16 meters and 12 meters.

The total area of these 2 parks is:

8^2*pi + 6^*pi = pi*(8^2 + 6^2) = pi*(64 + 36) = pi*100 = 314.1592654 meters.

The radius of this new park will be sqrt(A/pi) where A is the sum of the areas of the two smaller parks.

This is derived from the formula for Area as follows:

A = pi*r^2
divide both sides of equation by pi to get:
A/pi = r^2
take the square root of both sides of the equation to get:
r = sqrt(A/pi)

This means that r = sqrt((100*pi)/pi) = sqrt(100) = 10.

The radius of the new park should be 10.

10^2*pi = 100*pi = the sum of the areas of the two smaller parks that was previously calculated above.

radius of the new park is 10 meters is your answer.