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 π
.(1 point)
Responses

1,055.04 cubic centimeters
1,055.04 cubic centimeters

615.44 cubic centimeters
615.44 cubic centimeters

12,660.48 cubic centimeters
12,660.48 cubic centimeters

7,385.28 cubic centimeters

Answer 1

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**.