A cylinder has a radius of 7 cm and the area of its curved surface is 396 cm². The volume of the cylinder is:

The correct option is 1386 cm³.

To find the volume of the cylinder, we can follow these steps:

Step 1: Identify the given information.
Let $r$ be the radius of the cylinder, $h$ be its height, and $A$ be the curved surface area.
Given:
Radius ($r$) = 7 cm
Curved Surface Area ($A$) = 396 cm²
We will use the value of $\pi \approx \frac{22}{7}$ for our calculations.

Step 2: Find the height ($h$) of the cylinder using the curved surface area.
The formula for the curved surface area of a cylinder is:

$A=2\pi rh$

Substitute the given values into the formula to solve for $h$:

$396=2\times \frac{22}{7}\times 7\times h$

Simplify the equation by cancelling the common factor of 7 in the numerator and denominator:

$396=44\times h$

Solve for $h$:

$h=\frac{396}{44}$

$h=9\text{cm}$

Step 3: Calculate the volume ($V$) of the cylinder.
The formula for the volume of a cylinder is:

$V=\pi r^{2}h$

Substitute the values of $r=7\text{cm}$ and $h=9\text{cm}$ into the formula:

$V=\frac{22}{7}\times 7^2\times 9$

$V=\frac{22}{7}\times 49\times 9$

Simplify the equation:

$V=22\times 7\times 9$

$V=154\times 9$

$V=1386{\text{cm}}^3$

Therefore, the volume of the cylinder is 1386 cm³.