akathuria19
  • akathuria19
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.
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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akathuria19
  • akathuria19
arivillafana
  • 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(:
arivillafana
  • 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.

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akathuria19
  • akathuria19
How do I set this equation up though?
anonymous
  • anonymous
question is incomplete. cylinder can be of any dimensions.
anonymous
  • anonymous
|dw:1444281531164:dw|
akathuria19
  • 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)
anonymous
  • anonymous
\[\pi R^2H<\ \frac{ 1 }{ 3 } \pi r^2h,or~3 R^2H
akathuria19
  • akathuria19
It needs to be V(h) =
anonymous
  • anonymous
|dw:1444348030159:dw|
anonymous
  • 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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