geometry word problems - cylinder

Question

The height of a cylinder is H=10cm. If the radius of the base grows for 10cm, the volume will also grow for 1800πcm³. How long is the radius of the base?

Answer 1

 

 

 V = pi*H*r^2

 

     = pi*10* r^2

 

 

   V+1800*pi = pi*10*(r+10)^2

 

   pi*10*r^2+ 1800*pi = pi*10*(r^2 + 20r+ 100)

 

10*r^2 + 1800 = 10*(r^2 + 20r+100)

 

 r^2 + 180 = r^2 + 20r + 100

 

 180 = 20r + 100

 

80 = 20r 

 

r = 4

 

 

The radius us 4.

 

 

CHECK:

The original volume is pi*16*10 = 160*pi

 

radius increases by 10:

  pi*(14)^2 * 10 = pi*196*10 = 1960*pi

 

1960*pi - 160 pi = 1800*pi