Question

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

To find the volume of the rectangular prism, we need to first find the dimensions of the base and height of the pyramid.

The volume of a rectangular pyramid is given by the formula:

V = (1/3) * base area * height

We are given that the volume of the pyramid is 480 in.3. Let the base area of the pyramid be A and the height be h.

480 = (1/3) * A * h

Solving for A * h, we get:

A * h = 480 * 3 = 1440 in.2

Since the base of the pyramid is a rectangle, the base area is given by length * width. Therefore, we can express the base area as:

A = l * w

Substitute the expression for A into the equation A * h = 1440:

l * w * h = 1440

Since the base and height of the prism are congruent to the pyramid, we know that l = w = h.

Therefore, we have:

h * h * h = 1440

h^3 = 1440

h = cube root of 1440 = 12

So, the height and base dimensions of the prism are 12 in each.

Now, the volume of a rectangular prism is given by the formula:

V = l * w * h

Substitute the values of l, w, and h:

V = 12 * 12 * 12 = 1728 in.3

Therefore, the volume of the rectangular prism is 1728 in.3.