To find the volume of water that a pack of 12 cone-shaped cups will hold, we start by calculating the volume of a single cup and then multiply it by 12.
The formula for the volume \( V \) of a cone is given by:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( r \) is the radius of the cone,
- \( h \) is the height of the cone,
- \( \pi \) is approximately 3.14.
Given:
- Radius \( r = 7 \) cm
- Height \( h = 12 \) cm
Now we can substitute 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 that back into the equation:
\[ V = \frac{1}{3} \times 3.14 \times 49 \times 12 \]
Calculating \( 49 \times 12 \):
\[ 49 \times 12 = 588 \]
Now substituting that back into the equation:
\[ V = \frac{1}{3} \times 3.14 \times 588 \]
Now calculate \( 3.14 \times 588 \):
\[ 3.14 \times 588 \approx 1846.32 \]
Now calculate \( \frac{1846.32}{3} \):
\[ \frac{1846.32}{3} \approx 615.44 \text{ cubic centimeters} \]
This is the volume of one cup. To find the volume of a pack of 12 cups:
\[ \text{Total volume} = 615.44 \times 12 \]
Calculating that:
\[ 615.44 \times 12 \approx 7385.28 \text{ cubic centimeters} \]
Therefore, the total volume of water a pack of 12 cups will hold is:
7,385.28 cubic centimeters.
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