Question

A cylinder is inscribed in a cone as shown in the figure. The radius of the cone is 5 inches and the height is 9 inches. Express the volume, V, of the cylinder in terms of its height, h.

Answer 1

given this figure, we'll be able to know that Vcone = 1/3 (2pi(r))(H) = 56pi/3
Vcylinder = pi(r^2)(h) equating both equation we'll get

((1/3) (2)(pi)(r)(H))(4\9) = (pi)(r^2)(h) I hope that this will help you solve the problem(:

Answer 2

We know that the Vcylinder = 4/9 Vcone
and Vcylinder = (pi)(r^2)(h) and Vcone = 1/3(B)(H)
where: B= area of lower surface of cone and H=the height of cone.

Answer 3

How do I set this equation up though?

Answer 4

question is incomplete.
cylinder can be of any dimensions.

Answer 5

I'm confused on how to find the Volume in terms of its height...I understand that V of a cylinder is (pi)rh and volume of a cone is (pi)r^2(h/3)

Answer 6

\[\pi R^2H<\ \frac{ 1 }{ 3 } \pi r^2h,or~3 R^2H<r^2h \]
where Ris radius and H is height of cylinder.
and r is radius of cone ,h the height of cylinder
i think question should be cylinder of maximum volume.

Answer 7

It needs to be V(h) =

Answer 8

\[Volume V=\pi \left( \frac{ 5 }{ 9 }\left( 9-h \right) \right)^2h=\frac{ 25 }{ 81 } \pi h \left( 9-h \right)^2\]