Question: Problem 12:
(first taught in
lesson 98)
Calculate the volume of this solid.
8
23
After you enter your answer press GO.
volume =
Graph shape: a cylinder in the center with radius 8 and height 23; position_hint centerSolve
1. **State the problem:** Calculate the volume of a cylinder with radius $8$ and height $23$.
2. **Formula for the volume of a cylinder:**
$$V = \pi r^2 h$$
where $r$ is the radius and $h$ is the height.
3. **Substitute the given values:**
$$V = \pi \times 8^2 \times 23$$
4. **Calculate the square of the radius:**
$$8^2 = 64$$
5. **Multiply the values:**
$$V = \pi \times 64 \times 23$$
6. **Multiply $64$ and $23$:**
$$64 \times 23 = 1472$$
7. **Final volume expression:**
$$V = 1472 \pi$$
8. **Approximate the volume using $\pi \approx 3.1416$:**
$$V \approx 1472 \times 3.1416 = 4624.77$$
**Answer:** The volume of the cylinder is $$1472 \pi$$ cubic units or approximately $$4624.77$$ cubic units.