Question

Paper water cups in the shape of a cone have a radius of 7 centimeters and a height of 12 centimeters. Cups come in packs of 12. What volume of water will a pack of 12 cups hold? Use 3.14 for n.
(1 point)
• 1,055.04 cubic centimeters
• 7,385.28 cubic centimeters
• 615.44 cubic centimeters
• 12,660.48 cubic centimeters

Answer 1

To find the volume of one cone-shaped paper 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 \( r = 7 \) centimeters
- Height \( h = 12 \) centimeters

First, we substitute the 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 we can calculate the volume:

\[
V = \frac{1}{3} \times 3.14 \times 588
\]

Calculating \( 3.14 \times 588 \):

\[
3.14 \times 588 \approx 1846.32
\]

Now dividing by 3:

\[
V \approx \frac{1846.32}{3} \approx 615.44 \text{ cubic centimeters}
\]

This is the volume of one cup. Since the cups come in packs of 12, the total volume for 12 cups is:

\[
\text{Total Volume} = 615.44 \times 12
\]

Calculating \( 615.44 \times 12 \):

\[
615.44 \times 12 \approx 7385.28 \text{ cubic centimeters}
\]

Therefore, the total volume of water that a pack of 12 cups will hold is:

\[
\text{Total Volume} \approx 7,385.28 \text{ cubic centimeters}
\]

The correct answer is **7,385.28 cubic centimeters**.