The diameter of a circle is 16. By what number must the radius be decreased in order to decrease the area of the circle by 48 pi?

Guest Nov 6, 2017

#1**+1 **

The diameter of a circle is 16. By what number must the radius be decreased in order to decrease the area of the circle by 48 pi?

I really am not sure what you are asking.....

The original area is pi*64 if you want to decrease this by 48pi then the new area must be 16pi units^2

So the radius would have to be 4 units, the diameter would be 8 units.

This is half of the orginal diameter.

Melody
Nov 6, 2017

#2**+1 **

The current radius is diameter/ 2 = 16/ 2 = 8

And area = pi * r^2

So....the current area is pi (8)^2 = 64pi units^2

Reducing by 48 pi units^2 means that he new area is [ 64 pi - 48 pi ] = 16 pi units^2

So......16 pi = pi (r^2) .....divide both sides by pi ......

16 = r^2 ⇒ 4 = r

So....the current radius must be halved to reduce the area by 48 pi units^2

CPhill
Nov 6, 2017