The radius of base of cone is 3.5 cm and height is 9 cm. Its volume is `:`

Options

A. 36.75 `pi `
B. 110.25 `pi`
C. 330.75 `pi `
D. None of these

Answer

To find the volume of the cone, we will use the formula for the volume of a cone, which is given by:

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

Where:
- \( V \) is the volume of the cone,
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone,
- \( \pi \) is a constant approximately equal to 3.14.

### Step 1: Identify the given values
- Radius \( r = 3.5 \) cm
- Height \( h = 9 \) cm

### Step 2: Substitute the values into the formula
\[ V = \frac{1}{3} \pi (3.5)^2 (9) \]

### Step 3: Calculate \( r^2 \)
\[ (3.5)^2 = 12.25 \]

### Step 4: Substitute \( r^2 \) back into the volume formula
\[ V = \frac{1}{3} \pi (12.25) (9) \]

### Step 5: Calculate \( 12.25 \times 9 \)
\[ 12.25 \times 9 = 110.25 \]

### Step 6: Substitute this value back into the volume formula
\[ V = \frac{1}{3} \pi (110.25) \]

### Step 7: Calculate \( \frac{110.25}{3} \)
\[ \frac{110.25}{3} = 36.75 \]

### Step 8: Multiply by \( \pi \)
\[ V = 36.75 \pi \]

### Step 9: Approximate \( \pi \) to find the numerical value
Using \( \pi \approx 3.14 \):
\[ V \approx 36.75 \times 3.14 \approx 115.725 \text{ cm}^3 \]

### Final Answer
The volume of the cone is approximately \( 115.73 \text{ cm}^3 \) when rounded to two decimal places.

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