two small parks of diameter 16m , 12 m are to be replaced by a bigger circular park. what would be the diameter of this new park, if the new park has to occupy the same space as the two small parks?

Question

two small parks of diameter 16m , 12 m are to be replaced by a bigger circular park. what would be the diameter of this new park, if the new park has  to occupy the same space as the two small parks?

anonymous · Answer

are the two small parks squares?

anonymous · Answer

small circular parks

anonymous · Answer

and the options are a.30m   b .20.m  c.40 m  d. 50m

anonymous · Answer

Well area of a circle is pi*r^2.
And diameter is twice as big as the radius.
So add them both up individually.

pi*(16/2)^2 + pi*(12/2)^2.
=pi*8^2 +pi* 6^2
=pi*64 + pi* 36
= 64pi+36pi.
=100pi

The total area of the two small parks is 100pi.

So you need to find a new park with the same area.

Area=Pi*r^2. 
100pi=pi*r^2

Divide both sides by pi
100=r^2.

Square root both sides
r=10.

And since the radius is half the distance of the diameter, you multiply it by 2.

The answer is b. 20 m

dumbcow · Answer

it occupies same space so the area of the larger park must equal the sum of the smaller parks areas
A = pi*r^2
park1 area = 8^2 pi = 64pi
park2 area = 6^2 pi= 36pi
sum = 64pi + 36pi = 100pi
Area larger park = pir^2 = 100pi
r^2 = 100
r=10
diameter = 20

anonymous · Answer

thanks guys.....