The volume of a right circular cylinder of length 1.2 metres is 4620 cm³. What is the curved surface area (in cm²) of the cylinder ? (Take $\pi =\frac{22}{7}$)

The correct option is 2640.

We are given the following values for a right circular cylinder:

Length/Height of the cylinder, $h=1.2\text{metres}$

Converting height to centimetres ($1\text{metre}=100\text{cm}$):

$h=1.2\times 100=120\text{cm}$

Volume of the cylinder, $V=4620{\text{cm}}^3$

Value of $\pi =\frac{22}{7}$

Step 1: Find the radius ($r$) of the cylinder.

The formula for the volume of a cylinder is:

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

Substitute the given values into the formula:

$4620=\frac{22}{7}\times r^2\times 120$

Rearranging to solve for $r^2$:

$r^2=\frac{4620\times 7}{22\times 120}$

$r^2=\frac{32340}{2640}=12.25$

Taking the square root on both sides:

$r=\sqrt{12.25}=3.5\text{cm}$

Step 2: Calculate the curved surface area (CSA) of the cylinder.

The formula for the curved surface area of a cylinder is:

$\text{CSA}=2\pi rh$

Substitute the values of $\pi$, $r$, and $h$:

$\text{CSA}=2\times \frac{22}{7}\times 3.5\times 120$

$\text{CSA}=2\times 22\times 0.5\times 120$

$\text{CSA}=2640{\text{cm}}^2$

Thus, the curved surface area of the cylinder is 2640 cm².