To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid:
\[ V = \frac{1}{3} \times B \times h \]
where:
- \( V \) is the volume,
- \( B \) is the area of the base, and
- \( h \) is the height of the pyramid.
Step 1: Calculate the area of the base
The base of the rectangular pyramid is a rectangle with length (\( l \)) and width (\( w \)). The area (\( B \)) can be calculated using the formula:
\[ B = l \times w \]
Given:
- Length (\( l \)) = 7 cm
- Width (\( w \)) = 9 cm
Calculating \( B \):
\[ B = 7 , \text{cm} \times 9 , \text{cm} = 63 , \text{cm}^2 \]
Step 2: Plug the values into the volume formula and solve for height
We know the volume \( V \) is 231 cubic centimeters. Now, we can use the volume formula:
\[ 231 = \frac{1}{3} \times 63 \times h \]
Step 3: Multiply both sides by 3 to eliminate the fraction
\[ 3 \times 231 = 63 \times h \]
Calculating the left side:
\[ 693 = 63 \times h \]
Step 4: Solve for \( h \)
Now, we divide both sides by 63:
\[ h = \frac{693}{63} \]
Calculating \( h \):
\[ h = 11 , \text{cm} \]
Conclusion
The height of the pyramid is \( 11 , \text{cm} \).
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