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

Geometric formulae, word problems, theorems and proofs, etc.
little_dragon
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### A cone is divided into parts A and B; height same for each

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.

DAiv
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Joined: Tue Dec 16, 2008 7:47 pm
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### Re: A cone is divided into parts A and B; height same for each

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.
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).

DAiv

little_dragon
Posts: 226
Joined: Mon Dec 08, 2008 5:18 pm
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### Re: A cone is divided into parts A and B; height same for each

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!!!!!!