The curved surface area of a right circular cylinder of height 56 cm is 1408 cm². Find the diameter of the base of the cylinder.

To find the diameter of the base of the cylinder, we can use the formula for the curved surface area (CSA) of a right circular cylinder.

The formula for the curved surface area of a cylinder is:
$\mathrm{CSA}=2\pi rh$
where:
- $r$ is the radius of the base of the cylinder,
- $h$ is the height of the cylinder,
- $\pi$ is approximately equal to $\frac{22}{7}$.

From the problem, we are given:
- Height, $h=56cm$
- Curved surface area, $\mathrm{CSA}=1408<span>cm</span>²$

Substituting the given values into the formula:
$1408=2\times \frac{22}{7}\times r\times 56$

Simplify the right side of the equation by dividing 56 by 7:
$1408=2\times 22\times r\times 8$

Multiply the constants:
$1408=352\times r$

Solve for the radius $r$:
$r=\frac{1408}{352}$
$r=4cm$

The diameter ($d$) of the base is twice the radius:
$d=2r$
$d=2\times 4cm=8cm$

Now, we convert the diameter from centimeters to meters to match the given options. Since $1m=100cm$:
$d=\frac{8}{100}m=0.08m$

Therefore, the diameter of the base of the cylinder is 0.08m.