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Cone's Volume equal to Sphere's

Hi, I'm a little stumped by this question. I'm not entirely sure what I need to do but I've attempted it. Thank you for your help in advance.

There is a cone and a sphere.

The cone has a radius at its base of qmm and a height of hmm.

The radius of the sphere is 3qmm.

The volume of the cone and sphere is the same and I need to express h in the terms of q. What does that actually mean? Do I need to work out the volumes? Is this the right way to do it?

If I do, I get:

1/3 x π x q² x h = 4/3 x π x (3q)³

I can cancel out the π to get:

1/3 x q² x h = 4/3 x (3q)³

Then to simplify it:

1/3 x q² x h = 36q³

q² x h = 12q³

h = 12q

Is that right?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Cone's Volume equal to Sphere's

Nearly, but from 1/3 x q² x h = 36q³, you need to multiply both sides by 3, rather than dividing.

The final answer should be h = 108q.

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Why did the vector cross the road?
It wanted to be normal.