To find the volume of the composite figure made up of a rectangular prism and a rectangular pyramid, we need to calculate the volume of each individual shape and then add them together.
The volume of a rectangular prism can be calculated using the formula:
Volume of Prism = Length × Width × Height
where Length, Width, and Height refer to the dimensions of the prism.
Next, for the rectangular pyramid, the volume is calculated with the formula:
Volume of Pyramid = (1/3) × Base Area × Height
The Base Area of the pyramid is determined by multiplying the length and width of the base (which is the same as the dimensions of the top of the prism) and the Height indicates how tall the pyramid is from its base to the apex.
So, the total volume of the composite figure is simply the sum of these two volumes:
Total Volume = Volume of Prism + Volume of Pyramid
Using this approach allows us to find the total space occupied by both the prism and the pyramid combined.