A square pyramid has a height of 9 units and a volume of 147 units3. If a square prism has the same base area and volume as the square pyramid, what is its height? 1 unit 3 units 6 units 9 units

  3 units

Step-by-step explanation:

The volume of the pyramid is given by the formula ...

  V = 1/3Bh

where B is the base area and h is the height.

Filling in the given numbers, we find the base area to be ...

  147 = (1/3)B(9)

  49 = B . . . . . . . divide by 3

The square prism with the same volume will have a height given by ...

  V = Bh

  147 = 49h . . . . . . . fill in the known numbers

  147/49 = h = 3 . . . divide by 49

The square prism has a height of 3 units.

"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).

step-by-step explanation: