Question

The volume of a rectangular pyramid is 1020 unitscubed
3
. If the length of the rectangular base measures 10 units and the width of the rectangular base measures 18 units, find the height of the pyramid.

Answer 1

To find the height of the rectangular pyramid given its volume, you can use the formula for the volume of a pyramid:

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

The base area of a rectangular base can be calculated as:

\[
\text{Base Area} = \text{Length} \times \text{Width}
\]

In this case, the length is 10 units and the width is 18 units:

\[
\text{Base Area} = 10 \times 18 = 180 \text{ square units}
\]

Now, substituting the volume \(V = 1020\) cubic units and the base area into the volume formula:

\[
1020 = \frac{1}{3} \times 180 \times h
\]

To isolate \(h\) (the height), first multiply both sides by 3:

\[
3060 = 180 \times h
\]

Next, divide both sides by 180:

\[
h = \frac{3060}{180}
\]

Calculating this gives:

\[
h = 17 \text{ units}
\]

Thus, the height of the pyramid is \( \boxed{17} \) units.