To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid. The formula is:
\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
First, let's find the area of the base. The base is a rectangle, so we can calculate its area by multiplying the length and the width.
Given:
- Length = 7 cm
- Width = 9 cm
Now, we calculate the base area:
\[ \text{Base Area} = \text{Length} \times \text{Width} = 7 , \text{cm} \times 9 , \text{cm} = 63 , \text{cm}^2 \]
Next, we know the volume of the pyramid is 231 cubic centimeters. We can plug the base area into the volume formula and solve for the height.
The volume formula becomes:
\[ 231 = \frac{1}{3} \times 63 \times \text{Height} \]
To eliminate the fraction, we can multiply both sides by 3:
\[ 231 \times 3 = 63 \times \text{Height} \]
Calculating the left side gives us:
\[ 693 = 63 \times \text{Height} \]
Now we need to isolate the height. We can do this by dividing both sides by 63:
\[ \text{Height} = \frac{693}{63} \]
Now we just perform the division.
\[ \text{Height} = 11 , \text{cm} \]
So, the height of the pyramid is 11 cm.
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