Determine, to the nearest hundredth, the volume of the given pyramid.
The volume of a pyramid is one-third the area of the base 𝐵 times the height ℎ. Therefore, using our diagram, we need to find the area of the base and the height of our pyramid. We’ll put that into our formula and find the volume.
Here we have a base that’s a rectangle that’s six centimeters by four centimeters. Therefore, to find the area of the base, we need to take length times width. Six centimeters times four centimeters is equal to twenty-four centimeters squared.
Therefore, all that we have left to find is the height. In looking at our pyramid, we can see that that is nine centimeters. That’s our height. So we have one-third times twenty-four centimeters squared times nine centimeters. One-third times twenty-four times nine is seventy-two. Now it says to round to the nearest hundredth, which is two decimal places. So we could add point zero zero. That’s the same as seventy-two. And then centimeters squared times centimeters gives us centimeters cubed.
Therefore, the volume of this pyramid is seventy-two point zero zero centimeters cubed.