Determine, to the nearest hundredth, the volume of the given solid.
The solid in the diagram is made up of two pyramids which share a common base; it’s this rectangle here. We need to calculate the volume of each pyramid and add them together. The volume of a pyramid is calculated using the formula: volume equals one-third multiplied by 𝐵 multiplied by ℎ, where 𝐵 is the base area of the pyramid and ℎ is the perpendicular height. Remember, these two pyramids have the same base, so we’ll only calculate its area once.
The dimensions of the rectangle are 14 meters and 20 meters. Therefore, the base area is 14 multiplied by 20 which is 280, and the units for this will be meters squared.
Now let’s calculate the volume of the solid. For the upper pyramid, the height is 17, so the volume will be one-third multiplied by the base area, 280, multiplied by 17. For the lower pyramid, the height is 18. So the volume will be one-third multiplied by the base area, 280, multiplied by 18. Then we add these two volumes together to give the total. The first volume is 4760 over three and the second is 1680. This gives a total volume of 9800 over three.
The question has asked for the volume, not as a fraction but as a decimal to the nearest hundredth, so we need to evaluate this. As a decimal, the volume is 3266.6 recurring. And if we round this to the nearest hundredth, we have the total volume is 3266.67, and the units for this volume are meters cubed.