A cone is divided into parts A and B; height same for each  TOPIC_SOLVED

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A cone is divided into parts A and B; height same for each

Postby little_dragon on Fri Jan 30, 2009 1:43 am

A cone is divided into parts A and B. The vertical heights of A and B are equal. The volume of cone A is x cm^3. Express the volume of the whole cone in terms of x.

I can use 22/7 for pi, and I know V = (1/3)bh, with b = pir^2. But I have no idea what to do after that. :shock: :confused:
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Re: A cone is divided into parts A and B; height same for each  TOPIC_SOLVED

Postby DAiv on Fri Jan 30, 2009 8:22 am

little_dragon wrote:A cone is divided into parts A and B. The vertical heights of A and B are equal. The volume of cone A is x cm^3. Express the volume of the whole cone in terms of x.

I can use 22/7 for pi, and I know V = (1/3)bh, with b = pir^2. But I have no idea what to do after that. :shock: :confused:


Draw a side-on diagram of the cones and you'll have two similar triangles, one inside the other. They've told you that the vertical heights of the two parts, A and B, are equal, so the larger triangle is twice has high as the smaller one. Label the height of the smaller one 'h' and half its base (the cone's radius) 'r'. Now, using your knowledge of the properties of similar triangles, you can find the radius of the larger triangle. Plug the height and radius of the larger cone into the volume equation and compare it to the volume of the smaller cone. Finally, state your answer in terms of x (the volume of the smaller cone).


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Re: A cone is divided into parts A and B; height same for each

Postby little_dragon on Sat Jan 31, 2009 8:01 pm

DAiv wrote:using your knowledge of the properties of similar triangles

I never would of thought of similar triangles, but that worked great. It was easy! Thanks!!!!!! :clap: :thumb:
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