To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
where \(V\) is the volume, the Base Area is the area of the base of the pyramid, and Height is the height of the pyramid.
Step 1: Calculate the Base Area
The base of the pyramid is a rectangle, and its area can be calculated using the formula:
\[ \text{Base Area} = \text{Length} \times \text{Width} \]
Given:
- Length = 7 cm
- Width = 9 cm
Now, plug in the values:
\[ \text{Base Area} = 7 , \text{cm} \times 9 , \text{cm} = 63 , \text{cm}^2 \]
Step 2: Use the Volume Formula
We know the volume \(V\) is 231 cubic centimeters, and we just calculated the base area. Now we can plug these values into the volume formula:
\[ 231 = \frac{1}{3} \times 63 \times \text{Height} \]
Step 3: Solve for Height
First, we need to isolate the height (let's call it \(h\)). To do this, we can start by multiplying both sides of the equation by 3 to get rid of the fraction:
\[ 3 \times 231 = 63 \times h \]
Calculating the left side:
\[ 693 = 63h \]
Next, we divide both sides by 63 to solve for \(h\):
\[ h = \frac{693}{63} \]
Step 4: Simplify the Division
Now we need to do the division:
\[ h = 11 , \text{cm} \]
Final Answer
The height of the pyramid is 11 centimeters.
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