A rectangular Pyramid has a volume of 10cm. What is the volume of a rectangular prism given it has a congruent base and height to the Pyramid

1 answer

The volume of a rectangular pyramid is given by the formula V = (1/3)Bh, where B is the area of the base and h is the height. Since the pyramid has a volume of 10cm, we can write:

10cm = (1/3)Bh

Multiplying both sides by 3, we get:

30cm = Bh

Since the base and height of the pyramid are congruent, we know that the base is a square. Let's say the length of one side of the square base is x. We can then write:

B = x^2

Substituting this into the equation above, we get:

30cm = x^2h

To find the volume of a rectangular prism with a congruent base and height, we just need to multiply the area of the base (which is x^2) by the height (which is h). So the volume of the rectangular prism is:

V = x^2h

But from the equation we derived above, we know that x^2h = 30cm. So the volume of the rectangular prism is 30cm.