The formula for the volume of a rectangular pyramid is:

$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$

Step 1: Identify the known values

• Length of the base ($l$) = 7 cm
• Width of the base ($w$) = 9 cm
• Volume ($V$) = 231 cm³

The base area is:

$\text{Base Area} = l \times w = 7 \times 9 = 63 \, \text{cm}^2$

Step 2: Solve for the height

Substitute into the volume formula:

$231 = \frac{1}{3} \times 63 \times h$

Simplify:

$231 = 21 \times h$

Solve for $h$:

$h = \frac{231}{21} = 11 \, \text{cm}$

Final Answer:

The height of the pyramid is 11 cm.

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Would you like a step-by-step explanation of another similar problem? Here are some related questions:

1. How do you find the volume of a triangular pyramid?
2. If the height were doubled, what would the new volume be?
3. How do you calculate the surface area of a rectangular pyramid?
4. What happens to the volume if the base length and width are halved?
5. How can this formula be applied to irregular pyramids?

Tip: Always confirm the base area calculation before solving for height in volume problems.