https://file.aiquickdraw.com/mathbot/file/1729151368974qqnjl8he.jpg

The problem involves finding the volume of a pyramid using the given formula:

\[
V = \frac{1}{3} B h
\]
Where:
- \( B \) is the area of the base.
- \( h \) is the height of the pyramid.

### Step 1: Calculate the area of the base (\( B \))
The base of the pyramid is a rectangle, with dimensions:
- Length = 8 m
- Width = 2 m

The area \( B \) of the base is:
\[
B = \text{Length} \times \text{Width} = 8 \, \text{m} \times 2 \, \text{m} = 16 \, \text{m}^2
\]

### Step 2: Use the formula for the volume
From the diagram, the height of the pyramid \( h \) is given as 6 m. Now, substitute the values into the formula:

\[
V = \frac{1}{3} \times 16 \, \text{m}^2 \times 6 \, \text{m}
\]

\[
V = \frac{1}{3} \times 96 \, \text{m}^3 = 32 \, \text{m}^3
\]

### Conclusion:
The volume of the pyramid is \( 32 \, \text{m}^3 \), which corresponds to answer choice **C**.

---

Would you like more details or have any questions on this? Here are five related questions:

1. How would the volume change if the height of the pyramid were doubled?
2. What is the formula for the volume of a pyramid with a triangular base?
3. How would you calculate the volume if the base were a different shape (e.g., a circle)?
4. Can you explain the relationship between the volume of a pyramid and a rectangular prism with the same base and height?
5. How does the formula for the volume of a pyramid differ from that of a cone?

**Tip:** When calculating the volume of pyramids, ensure you correctly identify the height, which is the perpendicular distance from the base to the apex (top point).

What is the volume of the pyramid using the given formula and dimensions: base length 8m, base width 2m, and height 6m?

Calculate the volume of a pyramid using the formula V = (1/3) * B * h. The base is a rectangle with dimensions 8m by 2m, and the height is 6m. Follow a step-by-step explanation for solving this geometry problem, ideal for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation