The curved surface area of a right circular cylinder of base radius 3 cm is `94.2 cm^(2)`. The volume (in `cm^(3))` of the cylinder is (take `pi = 3.14`)

Options

A. `113.04`
B. `138.6`
C. `141.3`
D. `125.6`

Answer

To find the volume of the cylinder given its curved surface area (CSA) and base radius, we can follow these steps:

### Step 1: Understand the formula for the curved surface area of a cylinder
The formula for the curved surface area (CSA) of a right circular cylinder is given by:
\[ \text{CSA} = 2 \pi r h \]
where \( r \) is the radius and \( h \) is the height of the cylinder.

### Step 2: Substitute the known values into the CSA formula
We know that the CSA is \( 94.2 \, \text{cm}^2 \) and the radius \( r \) is \( 3 \, \text{cm} \). Substituting these values into the formula, we get:
\[ 94.2 = 2 \pi (3) h \]

### Step 3: Simplify the equation
Now, simplify the equation:
\[ 94.2 = 6 \pi h \]

### Step 4: Solve for the height \( h \)
To find \( h \), we can rearrange the equation:
\[ h = \frac{94.2}{6 \pi} \]
Using \( \pi = 3.14 \):
\[ h = \frac{94.2}{6 \times 3.14} = \frac{94.2}{18.84} \approx 5 \, \text{cm} \]

### Step 5: Use the volume formula for the cylinder
The volume \( V \) of a cylinder is given by:
\[ V = \pi r^2 h \]
Substituting the values of \( r \) and \( h \):
\[ V = \pi (3^2) (5) = \pi (9)(5) = 45\pi \]

### Step 6: Calculate the volume using \( \pi = 3.14 \)
Now, substituting \( \pi = 3.14 \):
\[ V = 45 \times 3.14 = 141.3 \, \text{cm}^3 \]

### Final Answer
The volume of the cylinder is \( 141.3 \, \text{cm}^3 \).

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