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Prism M and pyramid N have the same base area and the same height. Cylinder P and prism Q have the same height and the same base
perimeter. Cone Z has the same base area as cylinder Y, but its height is three times the height of cylinder Y.
The figures
and
have the same volume.

Respuesta :

The figures cone Z and cylinder Y have the same volume.

Explanation:

The formula for volume of the cone Z is given by

[tex]$V=\frac{1}{3} \pi r^{2} h$[/tex]

The formula for volume of the cylinder Y is given by

[tex]$\mathrm{V}=\pi r^{2} \mathrm{h}$[/tex]

Since, it is given that Cone Z has the same base area as cylinder Y, but its height is three times the height of cylinder Y.

Thus, substituting [tex]h=3h[/tex] in the formula of volume of the cone Z, we get,

[tex]$V=\frac{1}{3} \pi r^{2} (3h)$[/tex]

Simplifying, we have,

[tex]$\mathrm{V}=\pi r^{2} \mathrm{h}$[/tex]

Hence, the volume of the cone Z = volume of the cylinder Y

Thus, the figures cone Z and cylinder Y have the same volume.

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Answer:

The figures cone Z and cylinder Y have the same volume.

Step-by-step explanation:

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