Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 11 feet cubed

Answer 1

Answer:

Start with the formulas for the volumes of the sphere and cyl. respectively:

Vs = (4/3)*pi*r^3                        Vc = pi*r^2*h

Here, sphere and cyl. have the same radius and height.  Thus, the diam. of the sphere, d = 2r, has the same value as does h.

Thus, Vs = (4/3)*pi*r^3    and     Vc = pi*r^2*(2r) = 50.  Thus, pi*r^3 = 50, or

                                                                                                    r^3 = 50/pi

Then Vs = (4/3)(pi)*(50/pi) = 200/3 ft^3

Unfortunately, this doesn't agree with any of the answer choices, 'though it's close to given choice 100/3 ft^3, off by a factor of 2.

The trick here is to eliminate variables (especially the cyl. ht., h) and to make appropriate substitutions.

Step-by-step explanation: