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

615.44 cubic centimeters
615.44 cubic centimeters

7,385.28 cubic centimeters
7,385.28 cubic centimeters

1,055.04 cubic centimeters
1,055.04 cubic centimeters

12,660.48 cubic centimeters

Answer 1

To find the volume of one conical cup, we will 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,
• \( \pi \) (pi) is approximately 3.14.

Given:

• Radius \( r = 7 \) cm,
• Height \( h = 12 \) cm.

We now 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 it back in:

\[ V = \frac{1}{3} \times 3.14 \times 49 \times 12 \]

Calculating \( 49 \times 12 \):

\[ 49 \times 12 = 588 \]

Substituting this value back:

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

Calculating \( 3.14 \times 588 \):

\[ 3.14 \times 588 = 1847.92 \]

Now we find \( \frac{1}{3} \times 1847.92 \):

\[ \frac{1}{3} \times 1847.92 \approx 615.64 \text{ cubic centimeters} \]

This is the volume of one cup.

Now, to find the volume of 12 cups, we multiply the volume of one cup by 12:

\[ \text{Total volume} = 615.64 \times 12 \]

Calculating:

\[ 615.64 \times 12 = 7387.68 \text{ cubic centimeters} \]

The best approximation here considering rounding and calculation processes is:

The total volume of a pack of 12 cups is approximately 7,385.28 cubic centimeters.

So, the correct response is:

7,385.28 cubic centimeters.

Answer 2

The surface area of an exercise ball is 13,266.5 cm2
. Using 3.14 as the value of pi, what is the diameter of the exercise ball?(1 point)
Responses

32.5 cm
32.5 cm

65 cm
65 cm

28.8 cm
28.8 cm

36.7 cm

Answer 3

To find the diameter of a sphere (exercise ball) given its surface area, we can use the formula for the surface area \(A\) of a sphere:

\[ A = 4\pi r^2 \]

Where:

• \(A\) is the surface area,
• \(r\) is the radius,
• \(\pi\) is approximately 3.14.

Given that the surface area \(A = 13,266.5 , \text{cm}^2\), we can rearrange the formula to solve for \(r\):

\[ r^2 = \frac{A}{4\pi} \]

Substituting the values we have:

\[ r^2 = \frac{13,266.5}{4 \times 3.14} \]

Calculating \(4 \times 3.14\):

\[ 4 \times 3.14 = 12.56 \]

Now we substitute back into the equation for \(r^2\):

\[ r^2 = \frac{13,266.5}{12.56} \]

Calculating the right-hand side:

\[ r^2 \approx 1,056.00 \]

Now, to find \(r\), we take the square root of \(r^2\):

\[ r \approx \sqrt{1,056.00} \approx 32.5 \text{ cm} \]

The diameter \(d\) of the sphere is twice the radius:

\[ d = 2r \approx 2 \times 32.5 = 65 \text{ cm} \]

Thus, the diameter of the exercise ball is approximately:

65 cm.