Question

The height of a cylinder is 14cm and its curved surface area is 264cm\(^2\). The volume of the cylinder (in cm\(^3\)) is:

• A. 308
• B. 396
• C. 1584
• D. 1232

Hint:

For problems involving the surface area and volume of a cylinder, use the formulas for C.S.A and volume, and relate the two using given parameters.

Answer 1

The Correct Option is B

Step 1: Formula for Curved Surface Area of Cylinder.
The formula for the curved surface area (C.S.A) of a cylinder is: \[ \text{C.S.A} = 2 \pi r h \] where \( r \) is the radius and \( h \) is the height. Given that C.S.A = 264 cm\(^2\) and \( h = 14 \) cm, we substitute the values into the formula: \[ 264 = 2 \times \frac{22}{7} \times r \times 14 \] Simplifying: \[ 264 = \frac{22}{7} \times 28 \times r \implies r = \frac{264 \times 7}{22 \times 28} = \frac{1848}{616} = 3 \] Thus, the radius \( r = 3 \) cm.

Step 2: Formula for Volume of Cylinder.
The volume \( V \) of the cylinder is given by: \[ V = \pi r^2 h \] Substituting \( r = 3 \) cm and \( h = 14 \) cm: \[ V = \frac{22}{7} \times 3^2 \times 14 = \frac{22}{7} \times 9 \times 14 = 396 \, \text{cm}^3 \]

Final Answer: \[ \boxed{396 \, \text{cm}^3} \]