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 Question:
We are given the volume of a cylinder and its base radius. We are required to calculate its curved surface area (CSA).

Step 2: Key Formula or Approach:
The volume \( V \) of a cylinder is given by:
\[ V = \pi r^2 h \]
The curved surface area (CSA) of a cylinder is given by:
\[ \text{CSA} = 2\pi rh \]
We can first find the height \( h \) using the volume formula and then compute the CSA.
Alternatively, we can express the curved surface area in terms of the volume:
\[ \text{CSA} = \frac{2 \times \text{Volume}}{r} \]

Step 3: Detailed Explanation:
1. Let the base radius of the cylinder be \( r = 3\text{ cm} \).
2. Let the volume of the cylinder be \( V = 396\text{ cm}^3 \).
3. Let the height of the cylinder be \( h \).
4. First, let us solve using the standard method by finding the height \( h \):
\[ V = \pi r^2 h \]
Substituting the given values and \( \pi = \frac{22}{7} \):
\[ 396 = \frac{22}{7} \times 3^2 \times h \]
\[ 396 = \frac{22}{7} \times 9 \times h \]
\[ 396 = \frac{198}{7} \times h \]
5. Solving for \( h \):
\[ h = 396 \times \frac{7}{198} = 2 \times 7 = 14\text{ cm} \]
6. Now, we use the height \( h = 14\text{ cm} \) to find the curved surface area (CSA):
\[ \text{CSA} = 2\pi rh \]
7. Substituting the values:
\[ \text{CSA} = 2 \times \frac{22}{7} \times 3 \times 14 \]
8. Simplifying the expression:
\[ \text{CSA} = 2 \times 22 \times 3 \times 2 \]
\[ \text{CSA} = 44 \times 6 = 264\text{ cm}^2 \]

Step 4: Final Answer:
The curved surface area of the cylinder is \( 264\text{ cm}^2 \), which corresponds to option (C).