Question

The volume of a cylinder having a base radius of 3 cm is 396 cm³. Find its curved surface area (in cm²). (Use $\pi = \frac{22}{7}$).

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

Answer 1

The Correct Option is B

To find the curved surface area of the cylinder, we first need to determine its height. The volume \( V \) of a cylinder is given by the formula:

\[ V = \pi r^2 h \]

where \( r \) is the base radius and \( h \) is the height. Given \( r = 3 \, \text{cm} \) and \( V = 396 \, \text{cm}^3 \), substituting into the formula gives:

\[ 396 = \frac{22}{7} \times 3^2 \times h \]

Simplify:

\[ 396 = \frac{22}{7} \times 9 \times h \]

\[ 396 = \frac{198}{7} \times h \]

Multiply both sides by 7 to clear the fraction:

\[ 396 \times 7 = 198h \]

\[ 2772 = 198h \]

Divide both sides by 198 to solve for \( h \):

\[ h = \frac{2772}{198} \]

\[ h = 14 \, \text{cm} \]

Now, the curved surface area \( \text{CSA} \) of a cylinder is given by:

\[ \text{CSA} = 2\pi rh \]

Substitute the known values \( r = 3 \, \text{cm}, h = 14 \, \text{cm}, \pi = \frac{22}{7} \):

\[ \text{CSA} = 2 \times \frac{22}{7} \times 3 \times 14 \]

\[ \text{CSA} = \frac{264}{7} \times 14 \]

\[ \text{CSA} = 264 \, \text{cm}^2 \]

Therefore, the curved surface area of the cylinder is 264 cm².

Answer 2

The volume of a cylinder is given by \(V = \pi r^2 h\), where \(r\) is the radius and \(h\) is the height. 

We are given \(V = 396\) cm³ and \(r = 3\) cm, and \(\pi = \frac{22}{7}\).

So, \(396 = \frac{22}{7} \times 3^2 \times h = \frac{22}{7} \times 9 \times h\).

\(h = \frac{396 \times 7}{22 \times 9} = \frac{396 \times 7}{198} = 2 \times 7 = 14\) cm.

The curved surface area of a cylinder is given by \(CSA = 2 \pi r h = 2 \times \frac{22}{7} \times 3 \times 14\).

\(CSA = 2 \times 22 \times 3 \times 2 = 264\) cm²