A hemispherical bowl of internal radius 6 cm contains alcohol. This alcohol is to be filled into cylindrical shaped small bottles of diameter 6 cm and height 1 cm. How many bottles will be needed to empty the bowl ?

Options

A. 36
B. 27
C. 16
D. 4

Answer

To solve the problem step by step, we will calculate the volume of the hemispherical bowl and the volume of one cylindrical bottle, and then determine how many bottles are needed to hold the alcohol from the bowl.

### Step 1: Calculate the volume of the hemispherical bowl

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 that the internal radius of the bowl is 6 cm:

\[ V = \frac{2}{3} \pi (6)^3 \]

Calculating \( (6)^3 \):

\[ (6)^3 = 216 \]

Now substituting back into the volume formula:

\[ V = \frac{2}{3} \pi (216) = \frac{432}{3} \pi = 144 \pi \, \text{cm}^3 \]

### Step 2: Calculate the volume of one cylindrical bottle

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

\[ V = \pi r^2 h \]

Where \( r \) is the radius and \( h \) is the height. The diameter of the bottle is given as 6 cm, so the radius \( r \) is:

\[ r = \frac{6}{2} = 3 \, \text{cm} \]

The height \( h \) of the bottle is given as 1 cm. Now substituting these values into the volume formula:

\[ V = \pi (3)^2 (1) = \pi (9) = 9 \pi \, \text{cm}^3 \]

### Step 3: Calculate the number of bottles needed

To find the number of bottles \( n \) needed to empty the bowl, we divide the volume of the hemispherical bowl by the volume of one bottle:

\[ n = \frac{\text{Volume of hemispherical bowl}}{\text{Volume of one bottle}} = \frac{144 \pi}{9 \pi} \]

The \( \pi \) cancels out:

\[ n = \frac{144}{9} = 16 \]

### Conclusion

Therefore, the number of bottles needed to empty the bowl is:

\[ \boxed{16} \]