The area of base of a conical drum is `44 m^(2)` and its height is 2.1 m. Find its volume.

Answer

To find the volume of a conical drum given the area of its base and its height, we can follow these steps:

### Step 1: Understand the formula for the volume of a cone.
The volume \( V \) of a cone is given by the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius of the base, and \( h \) is the height of the cone.

### Step 2: Use the area of the base to find \( r^2 \).
We know that the area of the base of the cone is given as \( 44 \, m^2 \). The area \( A \) of the base (which is circular) can be expressed as:
\[ A = \pi r^2 \]
Setting this equal to the given area:
\[ \pi r^2 = 44 \]
To find \( r^2 \), we rearrange this equation:
\[ r^2 = \frac{44}{\pi} \]

### Step 3: Substitute \( r^2 \) into the volume formula.
Now that we have \( r^2 \), we can substitute it into the volume formula:
\[ V = \frac{1}{3} \pi \left(\frac{44}{\pi}\right) h \]
Given that the height \( h \) is \( 2.1 \, m \), we substitute this value in:
\[ V = \frac{1}{3} \pi \left(\frac{44}{\pi}\right) (2.1) \]

### Step 4: Simplify the expression.
Notice that \( \pi \) in the numerator and denominator will cancel out:
\[ V = \frac{1}{3} \cdot 44 \cdot 2.1 \]

### Step 5: Calculate the volume.
Now, we need to calculate \( \frac{1}{3} \cdot 44 \cdot 2.1 \):
\[ V = \frac{44 \cdot 2.1}{3} \]
Calculating \( 44 \cdot 2.1 \):
\[ 44 \cdot 2.1 = 92.4 \]
Now divide by 3:
\[ V = \frac{92.4}{3} = 30.8 \]

### Final Answer:
Thus, the volume of the conical drum is:
\[ V = 30.8 \, m^3 \]

---