The curved surface area of a right circular cylinder of base radius 3 cm is 94.2 cm2. The volume (in cm3) of the cylinder is (Take $\pi$ = 3.14)

Question

Accepted Answer

To determine the volume of the right circular cylinder, we need to use the given information about the curved surface area and the base radius. Let's go through the calculations step by step to justify why Option 2 is the correct answer.

### Given:
- Curved Surface Area (CSA) of the cylinder = 94.2 cm²
- Base radius (r) = 3 cm
- $\pi$ = 3.14

### Formulae:
1. Curved Surface Area (CSA) of a cylinder = 2πrh
2. Volume (V) of a cylinder = πr²h

### Step-by-Step Calculation:

#### Step 1: Find the height (h) of the cylinder
Using the formula for the curved surface area:
$$ 2\pi rh = 94.2 $$

Substitute the known values:
$$ 2 \times 3.14 \times 3 \times h = 94.2 $$

$$ 18.84h = 94.2 $$

Solve for h:
$$ h = \frac{94.2}{18.84} $$

$$ h = 5 \, \text{cm} $$

#### Step 2: Calculate the volume of the cylinder
Using the formula for the volume:
$$ V = \pi r^2 h $$

Substitute the known values:
$$ V = 3.14 \times 3^2 \times 5 $$

$$ V = 3.14 \times 9 \times 5 $$

$$ V = 3.14 \times 45 $$

$$ V = 141.3 \, \text{cm}^3 $$

### Conclusion:
The calculated volume of the cylinder is 141.3 cm³, which matches Option 2.

### Explanation of Incorrect Options:
- **Option 1 (138.6 cm³):** This value is slightly less than the correct volume. It could result from a miscalculation or incorrect rounding during intermediate steps.
- **Option 3 (125.6 cm³):** This value is significantly lower than the correct volume, indicating a possible error in using the wrong formula or incorrect substitution of values.
- **Option 4 (113.04 cm³):** This value is much lower than the correct volume, suggesting a substantial error in the calculation process, possibly due to incorrect use of the curved surface area or volume formula.

In summary, the correct volume of the cylinder, based on the given curved surface area and base radius, is 141.3 cm³, which corresponds to Option 2.