Cones, Cylinders, & Spheres Online Practice

Question

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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

12,660.48 cubic centimeters
12,660.48 cubic centimeters

1,055.04 cubic centimeters
1,055.04 cubic centimeters

7,385.28 cubic centimeters
7,385.28 cubic centimeters

615.44 cubic centimeters

Answer 1

To find the volume of one cone-shaped paper cup, you 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 plug in these values:

\[ V = \frac{1}{3} \times 3.14 \times (7^2) \times 12 \]

Calculating \( 7^2 \): \[ 7^2 = 49 \]

Now substitute back into the equation: \[ V = \frac{1}{3} \times 3.14 \times 49 \times 12 \]

Calculating \( 49 \times 12 \): \[ 49 \times 12 = 588 \]

Now substitute that into the volume equation: \[ V = \frac{1}{3} \times 3.14 \times 588 \]

Calculating \( 3.14 \times 588 \): \[ 3.14 \times 588 = 1847.92 \]

Now, divide by 3: \[ V = \frac{1847.92}{3} \approx 615.64 \text{ cubic centimeters} \]

So the volume of one cup is approximately 615.64 cubic centimeters.

To find the volume of a pack of 12 cups: \[ \text{Volume of 12 cups} = 615.64 \times 12 \] \[ 615.64 \times 12 = 7387.68 \text{ cubic centimeters} \]

Thus, the total volume of water the pack of 12 cups will hold is approximately 7,387.68 cubic centimeters.

So the closest response is: 7,385.28 cubic centimeters.