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## akathuria19 one year ago 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.

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1. akathuria19

2. arivillafana

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(:

3. arivillafana

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.

4. akathuria19

How do I set this equation up though?

5. anonymous

question is incomplete. cylinder can be of any dimensions.

6. anonymous

|dw:1444281531164:dw|

7. akathuria19

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)

8. anonymous

$\pi R^2H<\ \frac{ 1 }{ 3 } \pi r^2h,or~3 R^2H<r^2h$ 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.

9. akathuria19

It needs to be V(h) =

10. anonymous

|dw:1444348030159:dw|

11. anonymous

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

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