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 pack of 12 cups hold? Use 3.14 for pi.

Answer 1

To determine the total volume of water that a pack of 12 conical cups can hold, we first need to find the volume of a single cone. The formula for the volume \( V \) of a cone is given by:

\[
V = \frac{1}{3} \pi r^2 h
\]

where \( r \) is the radius and \( h \) is the height.

Given:
- Radius \( r = 7 \) centimeters
- Height \( h = 12 \) centimeters
- Approximate \(\pi \) is given as \( 3.14 \)

Now we can calculate the volume of one cup:

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

Calculating \( 7^2 \):

\[
7^2 = 49
\]

Now substitute \( 49 \) back into the volume formula:

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

Now, calculate \( 49 \times 12 \):

\[
49 \times 12 = 588
\]

Now substitute \( 588 \) into the equation:

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

Next, calculate \( 3.14 \times 588 \):

\[
3.14 \times 588 = 1847.92
\]

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

\[
V = \frac{1847.92}{3} = 616.64
\]

Thus, the volume of one cup is \( 616.64 \) cubic centimeters.

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

\[
\text{Total Volume} = 616.64 \times 12
\]

Calculating this gives:

\[
\text{Total Volume} = 7399.68
\]

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

\[
\boxed{7399.68} \text{ cubic centimeters.}
\]