Asked by john
express the surface of a right circular cylinder a function of its volume assuming the height is constant
Answers
Answered by
MathMate
Let the height be h (constant).
First find radius in terms of V, volume.
Volume, V = πr²h
radius, r = √(V/(πh))
So the total surface area is obtained by substituting r in the following expression:
A(total)
=2πrh+2πr^2
=2π√(V/(πh))(√(V/(πh))+h)
which simplifies to
2√(V/h)*(√(V/h)+√(π)h)
First find radius in terms of V, volume.
Volume, V = πr²h
radius, r = √(V/(πh))
So the total surface area is obtained by substituting r in the following expression:
A(total)
=2πrh+2πr^2
=2π√(V/(πh))(√(V/(πh))+h)
which simplifies to
2√(V/h)*(√(V/h)+√(π)h)
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.