Question

The volume of a cylinder having base radius 3 cm is 396 \(\text{cm}^3\). Find its curved surface area (in \(\text{cm}^2\)). (Use \(\pi\) = 22/7)

• A. 280
• B. 301.5
• C. 264
• D. 320.6

Hint:

You can relate Volume and Curved Surface Area directly using:
\[ \text{CSA} = \frac{2V}{r} \]
Let's check this shortcut:
\[ \text{CSA} = \frac{2 \times 396}{3} = 2 \times 132 = 264\text{ cm}^2 \]
This formula bypasses the calculation of height \( h \), giving the answer directly.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A cylinder is a three-dimensional solid geometric figure with two parallel circular bases. Given its volume and base radius, we can determine its height. Once the height is known, it can be used along with the radius to compute the curved surface area (the area of the side surface excluding the circular bases).
Step 2: Key Formula or Approach:
- Volume of a cylinder ($V$): \[ V = \pi r^2 h \] - Curved Surface Area of a cylinder ($\text{CSA}$): \[ \text{CSA} = 2 \pi r h \] Where $r$ is the base radius and $h$ is the height of the cylinder.
Step 3: Detailed Explanation:
Given parameters: Radius ($r$) = $3 \text{ cm}$, Volume ($V$) = $396 \text{ cm}^3$, and $\pi = \frac{22}{7}$.
Substitute the given values into the volume formula to calculate the height ($h$): \[ 396 = \frac{22}{7} \times 3^2 \times h \] \[ 396 = \frac{22}{7} \times 9 \times h \] \[ 396 = \frac{198}{7} \times h \] Isolate $h$: \[ h = \frac{396 \times 7}{198} \] \[ h = 2 \times 7 = 14 \text{ cm} \] Now, substitute $r = 3 \text{ cm}$ and $h = 14 \text{ cm}$ into the Curved Surface Area formula: \[ \text{CSA} = 2 \times \frac{22}{7} \times 3 \times 14 \] Simplify the expression by dividing 14 by 7: \[ \text{CSA} = 2 \times 22 \times 3 \times 2 \] \[ \text{CSA} = 44 \times 6 = 264 \text{ cm}^2 \]
Step 4: Final Answer:
The curved surface area of the cylinder is 264 $\text{cm}^2$.