How does the volume of a cylinder change if the radius is quadrupled and the height is reduced to a third of its original size?

A. v = 1/3 pie r^2 * h

B. v = 2/3 pie r^2 * h

C. v = 4/3 pie r^2 * h

D. v = 16/3 pie r^2 * h

Hello there.

How does the volume of a cylinder change if the radius is quadrupled and the height is reduced to a third of its original size?

D. v = 16/3 pie r^2 * h

Oh yay, proportional thinking! (Vicious sarcasm). Alright, let's do this:

Volume of the cylinder = π (h) r^2

New volume = π (h/3) (4r) ^2

= (1/3) π (h) (16r^2)

=16 * (1/3) π (h) r^2

= (16/3) π (h) r^2

Therefore, it's D. Though it's spelled pi, and you should really use the ^ symbol.