CUET CUET General Test 2024 - The volume of a cylinder having base radius 3 cm is 396 cm³. Find its curved surface area (in cm²): | PYQs + Solutions

CUET General Test 2024

Geometry

Solids

Medium

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

280

301.5

264

320.6

Correct Option: 3

To find the curved surface area of the cylinder, we first need to determine its height using the volume formula for a cylinder, which is given by:

V = \pi r^2 h

Given that the volume

V = 396 \, \text{cm}^3

and the radius

r = 3 \, \text{cm}

, we can substitute these values into the formula:

396 = \pi (3^2) h

This simplifies to:

396 = 9\pi h

Now, solving for

h

h = \frac{396}{9\pi} = \frac{44}{\pi} \, \text{cm}

Next, we use the formula for the curved surface area (CSA) of a cylinder, which is:

CSA = 2\pi rh

Substituting the values of

r

and

h

CSA = 2\pi (3) \left(\frac{44}{\pi}\right)

This simplifies to:

CSA = 6 \cdot 44 = 264 \, \text{cm}^2

Thus, the curved surface area of the cylinder is

264 \, \text{cm}^2