The volume of a pyramid can be calculated using the formula V = (1/3) * base area * height.
In this case, the base area of the pyramid is given as 36 cm? and the height is given as 6 cm. So, we can calculate the volume of this pyramid as follows:
V1 = (1/3) * 36 cm? * 6 cm = 72 cm3.
Now, let's move on to the second pyramid. The base of the pyramid has a side length of 3 centimeters. Since it is a square base, the area can be calculated as the side length
squared. So, the base area is 3 cm * 3 cm = 9 cm?.
We know that the volume of the second pyramid is the same as the volume of the first pyramid, which is 72 cm3. Using the same formula, we can calculate the height of the second pyramid:
V2 = (1/3) * 9 cm? * height of the second pyramid.
Since V2 = V1, we can set up the equation:
72 cm = (1/3) * 9 cm? * height of the second pyramid.
To solve for the height of the second pyramid, we can rearrange the equation:
height of the second pyramid = (72 cm3 * 3) / (9 cm?).
Simplifying the expression, we get:
height of the second pyramid = 24 cm / 9 cm?.
So, the height of the second pyramid is approximately 2.67 cm.
Therefore, the volume of both pyramids is 72 cm and the height of the second pyramid is approximately 2.67 cm.