Question 239337
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.