Video Transcript
Determine, to the nearest hundredth, the volume of the given pyramid.
In order to find the volume of this rectangular-base pyramid, we can use the formula that the volume of a pyramid is equal to one-third times the area of the base times ℎ, which represents the height of the pyramid. If we take a look at the diagram, the value here of nine centimeters represents the height of the pyramid. The values of six centimeters and four centimeters represent the side lengths of the rectangle at the base. And so in order to apply the formula for the volume of the pyramid, we do know the height, but we need to work out the area of the base.
Since the base is a rectangle, then we can use the fact that the area of a rectangle is equal to the length multiplied by the width. And so for the rectangle, we’ll be multiplying six by four, which is 24. And the units here will be squared centimeters.
And so now we can apply the formula for the volume of the pyramid because we know both the area of the base and the height. This gives us that the volume is equal to one-third times 24 times nine. Simplifying this gives us an answer of 72.
We were asked for the answer to the nearest hundredth. And we can represent this by writing two decimal digits in the answer. Because this is a volume, our units will be cubed. And so we can say that the volume of this pyramid to the nearest hundredth is 72.00 cubic centimeters.
