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Prism Mand 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.
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The figures Cone Z and Cylinder Y have the same volume.

Explanation:

The volume of the cylinder is given by

The volume of the cone is given by

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".

Hence, substituting in the volume formula of the volume of the cone.

We get,

Volume of cone Z =

Cancelling the common term, we get,

Volume of cone Z =

Volume of cone Z = Volume of the cylinder Y

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

Therefore, the figure cone Z and cylinder Y have the same volume.

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

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