A rectangular prism has the volume of 10 cm what is the volume of the rectangular prism given in the congruent base and height of the pyramid
The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
If the prism has a volume of 10 cm^3, and the base and height of the pyramid are congruent, then the base and height of the pyramid are also l, w, and h.
Since the volume of the prism is given as 10 cm^3, and the volume of a pyramid is given by the formula V = (1/3)Bh, where B is the base area and h is the height, we must have 10 = (1/3)lwh.
Given that the base and height are congruent, we can substitute l for w and h in the formula. Therefore, we have 10 = (1/3)l^2h.
To find the volume of the pyramid, we need to solve for V = (1/3)l^2h.
Multiplying the equation by 3, we get 30 = l^2h.
Therefore, the volume of the rectangular prism given in the congruent base and height of the pyramid is 30 cm^3.