Question

A rectangular pyramid has a length of 10 cm and a width of 15 cm. Its volume is 900 cubic centimeters. Use the formula for the volume of a pyramid to calculate the height of this pyramid. Show your work.

Answer 1

To calculate the height of the pyramid, we need to use the formula for the volume of a pyramid, which is given by:

\[
V = \frac{1}{3} \times B \times h
\]

where:
- \( V \) is the volume of the pyramid,
- \( B \) is the area of the base,
- \( h \) is the height of the pyramid.

For a rectangular base, the area \( B \) can be calculated as:

\[
B = \text{length} \times \text{width}
\]

Given the dimensions of the base:
- Length (l) = 10 cm
- Width (w) = 15 cm

Calculating the area \( B \):

\[
B = 10 \, \text{cm} \times 15 \, \text{cm} = 150 \, \text{cm}^2
\]

Now, we know the volume \( V \) is given as 900 cubic centimeters. We can substitute \( V \) and \( B \) into the volume formula to find the height \( h \):

\[
900 = \frac{1}{3} \times 150 \times h
\]

Now we simplify the equation:

\[
900 = 50h
\]

Next, we solve for \( h \):

\[
h = \frac{900}{50} = 18 \, \text{cm}
\]

Thus, the height of the pyramid is:

\[
\boxed{18 \, \text{cm}}
\]