Posted by Barb on .
A right circular cone has a volume of 140 in^3. The height of the cone is the same length as the diameter of the base. Find the radius and height.

Math  Please Help 
Jeff,
We know the formula for the Volume of a Right Circular Cone is given by
V=(1/3)*pi*r^2*h
V=140 in^3
The height of the cone = diameter of the base. The diameter = 2 times the radius, so h = 2r
The formula for Volume can now be written as
V=(1/3)*pi*r^2*(2r)
which simplifies to
V=(2/3)*pi*r^3
You plug in 140 in^3 for V and solve for r. Then you can plug the value you find for r into the equation h=2r 
Math  Please Help 
Reiny,
V = (1/3 π r^2 h , but h = 2r
3V = π r^2 (2r) = 2π r^3
420 = 2πr^3
r^3 = 210/π
r = (210/π)^(1/3) = 4.0584
r = 4.0584
h = 8.11683
check:
V = (1/3)π(4.0584)^2 (8.11683) = 139.9989.. , not bad