Question: The formula for the volume of a pyramid is $V = \frac{1}{3} Bh$, where $B$ is the area of the base of the pyramid and $h$ is the height of the pyramid.
What is the volume of this pyramid in cubic inches?
$8$ in.
$5$ in.
$6$ in.
position_hint: center
Type the answer in the box.
cubic inches
1. **State the problem:** We need to find the volume $V$ of a pyramid with given dimensions.
2. **Identify the formula:** The volume of a pyramid is given by $$V = \frac{1}{3} B h$$ where $B$ is the area of the base and $h$ is the height.
3. **Find the base area $B$:** The base is a rectangle with length $8$ inches and width $5$ inches.
$$B = 8 \times 5 = 40 \text{ square inches}$$
4. **Identify the height $h$:** The height of the pyramid is given as $6$ inches.
5. **Calculate the volume:** Substitute $B = 40$ and $h = 6$ into the formula:
$$V = \frac{1}{3} \times 40 \times 6$$
6. **Simplify the multiplication:**
$$V = \frac{1}{3} \times 240$$
7. **Divide to find the volume:**
$$V = \cancel{\frac{1}{3}} \times 240 = 80$$
8. **Final answer:** The volume of the pyramid is **80 cubic inches**.