Question

the volume of a cylinder is 24 π cubic feet.what is the volume of a cone having the same base and same height?

Answer 1

$\bf \stackrel{\textit{volume of a cylinder}}{V=\pi r^2 h}~\hspace{7em}\stackrel{\textit{volume of a cone}}{V=\cfrac{\pi r^2 h}{3}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of a cylinder}}{V=24\pi }~\hspace{7em}\stackrel{\textit{volume of a cone}}{V=\cfrac{24\pi }{3}}\implies V=8\pi$

notice the volumes, the cone's volume is really one-third that of the cylinder, assuming "h"eight and "r"adius is the same on both.

Answer 2

The volume of a cone having the same base and same height as of cylinder is 8π cubic feet.

What is volume of cone?

A cone is a solid that has a circular base and a single vertex. To calculate its volume you need to multiply the base area (area of a circle: π * r²) by height and by 1/3:

volume = (1/3) * π * r² * h.

It is given that the volume of cylinder 24 π cubic feet.

So, Volume of Cylinder= πr²h

          24 π   = πr²h

Now, The cone share the same height and base as of cylinder.

So,

Volume of Cone = 1/3 πr²h

                           = 1/3 (24 π)

                            = 8π cubic feet.

Thus Volume of Cone is 8π cubic feet.

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