Final answer:
To find the height of the rectangular pyramid, the volume formula V = (1/3)lwh is used. The given values of length 7 cm, width 9 cm, and volume 231 cm³ are substituted and solved to find the height, which is 11 cm.
Step-by-step explanation:
The student is asking to calculate the height of a rectangular pyramid given its length, width, and volume. To find the height of the pyramid, we use the formula for the volume of a pyramid, which is V = \( \frac{1}{3} \)lwh, where V is the volume, l is the length, w is the width, and h is the height.
Given:
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- Length (l) = 7 cm
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- Width (w) = 9 cm
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- Volume (V) = 231 cm³
Let's substitute the known values into the formula:
\( 231 = \frac{1}{3} \times 7 \times 9 \times h \)
Now we solve for h:
\( h = \frac{231 \times 3}{7 \times 9} \)
\( h = \frac{693}{63} \)
\( h = 11 cm \)
The height of the rectangular pyramid is 11 cm.