The height of a right circular cone is 6 cm and area of its base is `18.5 cm^(2)`. Find its volume.

Answer

To find the volume of the right circular cone, we can follow these steps:

### Step 1: Identify the given values
We know:
- Height (h) of the cone = 6 cm
- Area of the base (A) = 18.5 cm²

### Step 2: Use the formula for the area of the base to find the radius
The area of the base of a cone is given by the formula:
\[ A = \pi r^2 \]
Where \( r \) is the radius of the base.

We can rearrange this formula to find \( r^2 \):
\[ r^2 = \frac{A}{\pi} \]
Substituting the given area:
\[ r^2 = \frac{18.5}{\pi} \]

### Step 3: Use the volume formula for a cone
The volume (V) of a cone is given by the formula:
\[ V = \frac{1}{3} \pi r^2 h \]

### Step 4: Substitute the values into the volume formula
Now we can substitute \( r^2 \) and \( h \) into the volume formula:
\[ V = \frac{1}{3} \pi \left(\frac{18.5}{\pi}\right) \times 6 \]

### Step 5: Simplify the expression
Now, simplify the expression:
- The \( \pi \) in the numerator and denominator cancels out:
\[ V = \frac{1}{3} \times 18.5 \times 6 \]

### Step 6: Calculate the volume
Now, calculate the volume:
\[ V = \frac{1}{3} \times 18.5 \times 6 = \frac{111}{3} = 37 \, \text{cm}^3 \]

### Final Answer
The volume of the cone is \( 37 \, \text{cm}^3 \).

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