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?

Answer 1

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.

Answer 2

Does a pryamid have 1/3 of a rectangular pyramid.

Answer 3

Yes, a pyramid (with a rectangular base) has 1/3 the volume of a rectangular pyramid with the same base and height. This is because a rectangular pyramid has the same base as a rectangular prism, whose volume is given by V = bh (where b is the area of the base and h is the height). So the volume of a rectangular pyramid is given by (1/3)bh, where h is the height of the pyramid. If we compare this to the volume of a rectangular prism with the same base and height, we see that the prism has volume bh, which is three times the volume of the pyramid. Therefore, a pyramid has 1/3 the volume of a rectangular pyramid with the same base and height.