Question

The volume of a cylinder having base radius 3 cm is 396 cm³. Find its curved surface area (in cm²).

• A. 264
• B. 300
• C. 320
• D. 350

Answer 1

The Correct Option is A

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

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

where \( r \) is the radius and \( h \) is the height. Given \( V = 396 \, \text{cm}^3 \) and \( r = 3 \, \text{cm} \), we substitute to find \( h \):

\[ 396 = \pi \times 3^2 \times h \]

\[ 396 = 9\pi h \]

\[ h = \frac{396}{9\pi} \]

To simplify, we approximate \(\pi\) as 3.14:

\[ h = \frac{396}{28.26} \approx 14 \, \text{cm} \]

Next, we calculate the curved surface area (CSA) using:

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

Substitute \( r = 3 \, \text{cm} \) and \( h = 14 \, \text{cm} \):

\[ \text{CSA} = 2 \times \pi \times 3 \times 14 \]

\[ \text{CSA} = 84\pi \]

Using \(\pi \approx 3.14\), we calculate the CSA:

\[ \text{CSA} = 84 \times 3.14 = 263.76 \approx 264 \, \text{cm}^2 \]

Therefore, the curved surface area of the cylinder is \( 264 \, \text{cm}^2 \).