To find the volume of a single cone-shaped cup, we can use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately 3.14.
Given:
- Radius \( r = 7 \) cm
- Height \( h = 12 \) cm
Now, substituting these values into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (7^2) \times 12 \]
Calculating \( 7^2 \):
\[ 7^2 = 49 \]
Now substituting back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 49 \times 12 \]
Calculating \( 49 \times 12 \):
\[ 49 \times 12 = 588 \]
Now substituting back:
\[ V = \frac{1}{3} \times 3.14 \times 588 \]
Calculating \( 3.14 \times 588 \):
\[ 3.14 \times 588 = 1846.32 \]
Now dividing by 3:
\[ V = \frac{1846.32}{3} \approx 615.44 \text{ cubic centimeters} \]
This is the volume of one cup. Now, to find the volume of a pack of 12 cups:
\[ \text{Total volume} = 12 \times 615.44 = 7,385.28 \text{ cubic centimeters} \]
The correct response is:
7,385.28 cubic centimeters.