A rectangular pyramid has a volume of 10 cm ^3. What is the volume of a rectangular prism given it has a congruent base and height to the pyramid?
To find the volume of the rectangular prism, we need to find the volume of the base of the pyramid and multiply it by the height of the prism.
Since the base of the pyramid is a rectangle, we can find its area by dividing the volume of the pyramid by the height of the pyramid:
Volume of base = Volume of pyramid / height of pyramid
Volume of base = 10 cm^3 / 1 cm
Volume of base = 10 cm^2
Now, since the base of the rectangular prism is congruent to the base of the pyramid, the volume of the base of the prism will also be 10 cm^2.
Since the height of the prism is the same as the height of the pyramid, we can find the volume of the prism by multiplying the volume of the base by the height of the prism:
Volume of prism = Volume of base * height of prism
Volume of prism = 10 cm^2 * 1 cm
Volume of prism = 10 cm^3
Therefore, the volume of the rectangular prism is 10 cm^3.