Question

A rectangular prism has a base area of 15 cm and a congruent Pyramid has a volume of 20cm. What is the height of the rectangular prism?

Answer 1

There are a few different ways to approach this problem, but here's one possible method:

Let's start by drawing a diagram of the rectangular prism and pyramid:

```

+--------------+
/ /| /|
/ / | / |
/ / | / |
/ / | / |
+--------------+ |
| | |
| Pyramid | |
| | |
+--------------+ /
| / /
| / /
| / /
| / /
|/ /

```

We know that the base area of the rectangular prism is 15 cm, so let's call the length and width of the base "x" and "y", respectively. Then we can write:

xy = 15

Next, we know that the pyramid has a volume of 20 cm, and we're told that it's congruent (i.e. same size and shape) to the rectangular prism. Since the pyramid has one-third the volume of a rectangular prism with the same base and height, we can write:

(1/3)xyh = 20

where "h" is the height of the pyramid. Now we can solve for "h" in terms of "x" and "y":

h = (60/xy)

Substituting our expression for xy from the first equation, we get:

h = (60/15)

h = 4 cm

So the height of the rectangular prism is also 4 cm, since the pyramid and prism are congruent.