Asked by Barb
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.
Answers
Answered by
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
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
Answered by
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
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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.