To find the volume of one cone-shaped cup, we can use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height.
Given:
- Radius \( r = 7 \) cm
- Height \( h = 12 \) cm
- Using \( \pi \approx 3.14 \)
Now we can plug in the values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (7^2) \times 12 \]
Calculating \( r^2 \):
\[ 7^2 = 49 \]
Now plug this value 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 substitute this value into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 588 \]
Calculating \( 3.14 \times 588 \):
\[ 3.14 \times 588 = 1847.92 \]
Now, calculate \( \frac{1}{3} \times 1847.92 \):
\[ V \approx 616.64 \text{ cubic centimeters} \]
This is the volume of one cup. To find the volume of a pack of 12 cups, multiply the volume of one cup by 12:
\[ \text{Total Volume} = 616.64 \times 12 \approx 7399.68 \text{ cubic centimeters} \]
Rounding this value gives approximately 7,400 cubic centimeters.
Based on the options provided, it seems there might have been a small rounding issue, but the closest response to our computed total volume of 7399.68 cubic centimeters is 7,385.28 cubic centimeters.
Thus, the volume that a pack of 12 cups will hold is approximately 7,385.28 cubic centimeters.