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
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.
To find the volume of a rectangular prism given that it has a congruent base and height to the rectangular pyramid, we can use the formula:
Volume of a prism = Base area × Height
Since the base and height of the rectangular prism are congruent to the rectangular pyramid, we can use the same values.
We are given that the volume of the rectangular pyramid is 10 cm³. Therefore, the volume of the rectangular prism will also be 10 cm³.