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

Question

.(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.