To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid, which is given by:
\[ V = \frac{1}{3} \times B \times h \]
In this formula, \( V \) represents the volume of the pyramid, \( B \) is the area of the base, and \( h \) is the height. For a rectangular pyramid, the area of the base can be calculated by multiplying the length and width of the base. In this case, the base has a length of 7 cm and a width of 9 cm, which means the area \( B \) can be calculated as follows:
\[ B = \text{length} \times \text{width} = 7 , \text{cm} \times 9 , \text{cm} = 63 , \text{cm}^2 \]
Given that the volume \( V \) of the pyramid is 231 cubic centimeters, we can substitute the values of \( B \) and \( V \) into the volume formula to solve for the height \( h \):
\[ 231 = \frac{1}{3} \times 63 \times h \]
To isolate \( h \), we first simplify the equation. Multiplying both sides by 3 gives us:
\[ 693 = 63 \times h \]
Next, we can solve for \( h \) by dividing both sides by 63:
\[ h = \frac{693}{63} = 11 \]
Thus, the height \( h \) of the pyramid is 11 cm.
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