Question

The volume of the rectangular pyramid is 120 m to the third degree. The height is 15 m and the length of the base is 6 meters what is the width of the base of the rectangular pyramid?

Answer 1

To find the width of the base of the rectangular pyramid, we can use the formula for the volume of a pyramid:

\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

For a rectangular pyramid, the base area is calculated as:

\[
\text{Base Area} = \text{length} \times \text{width}
\]

Let \( w \) be the width of the base. Given:

- Volume \( V = 120 \, \text{m}^3 \)
- Height \( h = 15 \, \text{m} \)
- Length \( l = 6 \, \text{m} \)

We can substitute the values into the volume formula:

\[
120 = \frac{1}{3} \times (l \times w) \times h
\]

Substituting the known values:

\[
120 = \frac{1}{3} \times (6 \times w) \times 15
\]

Now, calculate the base area component:

\[
120 = \frac{1}{3} \times 90w
\]

Simplifying this:

\[
120 = 30w
\]

To find \( w \), divide both sides by 30:

\[
w = \frac{120}{30} = 4
\]

Therefore, the width of the base of the rectangular pyramid is:

\[
\boxed{4 \, \text{m}}
\]