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