https://file.aiquickdraw.com/mathbot/file/1728859849344cc0i9e08.jpg

Find the volume of the figure when 
b = 4 ft and h = 6 ft.

 

 ft3

The image depicts a square pyramid, with the base having side length \( b \) and height \( h \).

The formula to find the volume \( V \) of a pyramid is:

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

For a square base, the base area \( A \) is given by:

\[
A = b^2
\]

Substituting into the volume formula:

\[
V = \frac{1}{3} \times b^2 \times h
\]

Given \( b = 4 \, \text{ft} \) and \( h = 6 \, \text{ft} \):

\[
V = \frac{1}{3} \times 4^2 \times 6 = \frac{1}{3} \times 16 \times 6 = \frac{1}{3} \times 96 = 32 \, \text{ft}^3
\]

Thus, the volume of the pyramid is **32 cubic feet**.

Would you like more details or have any other questions?

Here are some follow-up questions to deepen understanding:
1. How does the volume formula change for other types of pyramids?
2. What would happen to the volume if the height doubled but the base stayed the same?
3. How is the formula for a cone's volume similar to that of a pyramid?
4. What is the significance of the \( \frac{1}{3} \) factor in the volume formula?
5. How would you calculate the surface area of this pyramid?

**Tip:** When dealing with pyramids, always verify the base shape and dimensions before applying the volume formula.

Find the volume of the figure when b = 4 ft and h = 6 ft.

Learn how to calculate the volume of a square pyramid with a base of 4 feet and height of 6 feet using geometry formulas. Step-by-step solution for understanding the volume theorem for pyramids, suitable for Grades 6-9.

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