A sphere is inscribed in a right circular cylinder . What is the ratio if the volume of the sphere to the volume of the cylinder?

Question

anonymous · Answer

Do you know the formulas for the volume of spheres and cylinders?

anonymous · Answer

Yes, V =πr^2h Cylinder. V = 4^3 π r Sphere

anonymous · Answer

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Since the sphere is inscribed within the cylinder, the sphere's diameter is equal to both the cylinder's height, and it's diamter

anonymous · Answer

okay…  How do we find the ratio through the formals. I can do it with numbers. but without I get really confused.

anonymous · Answer

Okay, so you have these two formulas for volume:

$$V_s = 4/3*\pi*(r_s)^3 $$
$$V_C = \pi*(r_C)^2*h_C$$

We know that $$D_s = D_C$$ and $$D_s = h_C$$

Also, the diameter is equal to the radius times two, so
$$r_C = D_C/2 $$ and $$r_s = D_s/2$$
Now that you can relate the dimensions of the cylinder to the sphere, you can take the ratio of the sphere's volume to the cylinder's volume:
$$ratio = V_s/V_C $$

anonymous · Answer

As a hint, try to find rC and hC in terms of rs.

That way, when you divide to find the ratio, the rs terms will all cancel out and you'll be left with a constant, which will be your ratio

anonymous · Answer

I think I got it now!  Thanks for your help! :)