Question: Problem 1: A pastry shop makes a large cone-shaped chocolate mold for a special event. The mold has an internal radius of 0.5 meters and a height of 1.8 meters.
a. How much chocolate (in cubic meters) can the mold hold when completely full?
1. **State the problem:** We need to find the volume of a cone-shaped mold with radius $r=0.5$ meters and height $h=1.8$ meters.
2. **Formula for the volume of a cone:**
$$V = \frac{1}{3} \pi r^2 h$$
This formula calculates the volume inside a cone using its radius and height.
3. **Substitute the given values:**
$$V = \frac{1}{3} \pi (0.5)^2 (1.8)$$
4. **Calculate the square of the radius:**
$$0.5^2 = 0.25$$
5. **Plug in the squared radius:**
$$V = \frac{1}{3} \pi (0.25) (1.8)$$
6. **Multiply $0.25$ and $1.8$:**
$$0.25 \times 1.8 = 0.45$$
7. **Volume expression becomes:**
$$V = \frac{1}{3} \pi (0.45)$$
8. **Multiply by $\frac{1}{3}$:**
$$V = \cancel{\frac{1}{3}} \pi \times \cancel{0.45}$$
Actually, multiply directly:
$$V = 0.15 \pi$$
9. **Calculate the numerical value using $\pi \approx 3.1416$:**
$$V \approx 0.15 \times 3.1416 = 0.47124$$
10. **Final answer:**
The mold can hold approximately
$$\boxed{0.471}$$ cubic meters of chocolate when completely full.