A rectangular pyramid has a volume of 480 in.3. If a rectangular prism has a base and height congruent to the pyramid, what is the volume of the prism?
Let's call the base of the rectangular pyramid "b" and the height "h". Then we know that the volume of the pyramid is:
V = (1/3)bh
We also know that this volume is equal to 480 in.3, so we can set up an equation:
(1/3)bh = 480
Now we need to find the volume of the rectangular prism that has the same base and height as the pyramid. Since the base is rectangular, we know that the area of the base is:
A = bh
And since the height of the prism is also "h", the volume is:
V = Ah = bhh
But we know that b = h (since the base and height are congruent), so we can simplify this to:
V = h^2h = h^3
So we need to find the value of "h" that makes the volume of the prism equal to the volume of the pyramid. We can solve for "h" in the equation we set up earlier:
(1/3)bh = 480
(1/3)(h^2)h = 480
h^3 = 1440
h = 12
Now we can find the volume of the rectangular prism:
V = h^3 = 12^3 = 1728 in.3
So the volume of the prism is 1728 cubic inches.
Does a pryamid have 1/3 of a rectangular pyramid.
To get the volume of the pyramid, we can use the formula:
Volume of a pyramid = (Base area * Height) / 3
Given that the volume of the pyramid is 480 in.3, we can rewrite the formula as:
480 = (Base area * Height) / 3
To find the volume of the prism, we need to know if the dimensions of the base and height of the prism are congruent to the pyramid. If they are, then the volume of the prism would be the same as the pyramid.
However, since it is not specified whether the dimensions of the base and height of the prism are congruent to the pyramid, we cannot determine the volume of the prism with the given information.