To find the total volume of water that a pack of 12 conical paper cups can hold, we first need to calculate the volume of a single cone and then multiply that by 12.
The formula for the volume \( V \) of a cone is:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( r \) is the radius of the cone,
- \( h \) is the height of the cone,
- \( \pi \) is approximately \( 3.14159 \).
Given:
- Radius \( r = 7 \) cm,
- Height \( h = 12 \) cm.
Now, substituting the values into the volume formula:
\[ V = \frac{1}{3} \pi (7^2) (12) \] \[ V = \frac{1}{3} \pi (49) (12) \] \[ V = \frac{1}{3} \pi (588) \] \[ V = 196 \pi \text{ cm}^3 \]
Using the approximation \( \pi \approx 3.14 \):
\[ V \approx 196 \times 3.14 \approx 615.44 \text{ cm}^3 \]
Now that we have the volume of one cup, we can calculate the total volume for 12 cups:
\[ \text{Total Volume} = 12 \times V \] \[ \text{Total Volume} \approx 12 \times 615.44 \text{ cm}^3 \approx 7385.28 \text{ cm}^3 \]
Thus, a pack of 12 cone-shaped paper cups can hold approximately 7385.28 cm³ of water.