A gigantic balloon used for a parade is shaped like an ice cream cone. The radius of the cone and the hemisphere is 12 feet. The height of the cone is 60 feet. If the balloon is filled with helium, how much helium will be needed to fill the balloon? Use 3.14 for pi. Show your work.

Question

What is the volume of the cone? Use 3.14 for pi and round your answer to the nearest tenth.

Answer 1

To find out the total volume of the balloon-shaped like an ice cream cone, we must calculate the volume of both the cone and the hemisphere on top of it.

Step 1: Calculate the Volume of the 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 of the base of the cone
• \( h \) is the height of the cone

Given:

• \( r = 12 \) feet
• \( h = 60 \) feet

Substituting the given values into the formula:

\[ V = \frac{1}{3} \times 3.14 \times (12)^2 \times 60 \]

Calculating \( (12)^2 \):

\[ (12)^2 = 144 \]

Now substituting \( 144 \) back into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times 144 \times 60 \]

Calculating \( 144 \times 60 \):

\[ 144 \times 60 = 8640 \]

Now substituting \( 8640 \) back into the formula:

\[ V = \frac{1}{3} \times 3.14 \times 8640 \]

Calculating \( \frac{1}{3} \times 8640 \):

\[ \frac{8640}{3} = 2880 \]

Now calculating the final volume of the cone:

\[ V = 3.14 \times 2880 \]

Calculating \( 3.14 \times 2880 \):

\[ 3.14 \times 2880 = 9043.2 \]

Thus, the volume of the cone is approximately \( 9043.2 \) cubic feet.

Step 2: Calculate the Volume of the Hemisphere

The formula for the volume \( V \) of a hemisphere is given by:

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

Where:

• \( r \) is the radius of the hemisphere

Given:

• \( r = 12 \) feet

Substituting the radius into the formula:

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

Calculating \( (12)^3 \):

\[ (12)^3 = 1728 \]

Now substituting \( 1728 \) back into the formula:

\[ V = \frac{2}{3} \times 3.14 \times 1728 \]

Calculating \( \frac{2}{3} \times 1728 \):

\[ \frac{2 \times 1728}{3} = \frac{3456}{3} = 1152 \]

Now calculating the final volume of the hemisphere:

\[ V = 3.14 \times 1152 \]

Calculating \( 3.14 \times 1152 \):

\[ 3.14 \times 1152 = 3628.8 \]

Step 3: Calculate Total Volume

The total volume of the balloon (cone + hemisphere) is:

\[ \text{Total Volume} = \text{Volume of Cone} + \text{Volume of Hemisphere} \]

Substituting the calculated volumes:

\[ \text{Total Volume} = 9043.2 + 3628.8 = 12672 \]

Final Answer

The total volume of helium needed to fill the balloon is approximately 12672 cubic feet.

• Volume of the cone: 9043.2 cubic feet (rounded to the nearest tenth).
• Total volume to fill the balloon: 12672 cubic feet.