SOLUTION: The volume of a cylinder is jointly proportional to the square of its radius and to its height. It's volume is 942cm^2 when its height is 3cm and its radius is 10 cm. The proportio

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The volume of a cylinder is jointly proportional to the square of its radius and to its height. It's volume is 942cm^2 when its height is 3cm and its radius is 10 cm. The proportio      Log On


   

Question 1039516: The volume of a cylinder is jointly proportional to the square of its radius and to its height. It's volume is 942cm^2 when its height is 3cm and its radius is 10 cm. The proportionality constant constant is k=3.14
a. what will be the radius if the volume is doubled?
b.What will happen to the volume if the radius is halved and while the height is quadrupled?
Answer by chen.aavaz(62) About Me  (Show Source):
You can put this solution on YOUR website!
a.
volume: V
radius: R
height: H
then
V=k%2AR%5E2%2AH
if
Vnew=2%2AV
and
Hnew=H (remains the same), then
Rnew%5E2=2%2AR%5E2
so
Rnew=R%2Asqrt%282%29
b.
Rnew=R%2F2
and
Hnew=H%2A4

Vnew=k%2A%28R%2F2%29%5E2%2AH%2A4=V
So it remains the same.