Radius/Area?

Question

I was wondering how to find the radius of the area. In my math book, it says this is how to solve it:
A= 3.14 r2 (squared)
256(3.14)=3.14 r2 (squared)
256= r2 (squared)
r=16


Any ideas? To me, this solution doesn't make sense. It will if someone can tell me why they got 16 and so on.

Thanks!

Answer 1

Area = pi x R x R

They solved for R

where area = 256

256 = 3.14 x RxR

R(squared) = 81

R = 9 (rounded) the actual answer was 9.02

If Area is 256PI, then R 16 using the methods shown.

Answer 2

Since both sides have a factor of 3.14 (or an approximation of "pi"), you can divide both sides by this value, and you end up with:

256 = r²

Since the square root of 256 is 16, the answer is r = 16.

Answer 3

The square root of 256 is 16.

Answer 4

You are talking about a circle which has an area of 256 pi.
The area of a circle is pi*r^2.
So 256pi = pi r^2
256 = r^2 [pi cancels out]
Take square root of both sides getting:
16 = r

Answer 5

im assuming the text gives you area = 256pi

then using the equation area = pi x radius^2

256 pi = pi r^2

divide both sides by pi

256 = r^2
square root both sides
r = square root 256
r = 16