The surface area of a solid cylinder of radius 2 cm and height 10 cm is equal to .......(mm)²

The correct option is 15072 mm².

To find the total surface area of the solid cylinder, we first need to convert the given dimensions from centimeters (cm) to millimeters (mm).

Given details:
Radius, $r=2\text{cm}$
Since $1\text{cm}=10\text{mm}$, we have:
$r=2\times 10\text{mm}=20\text{mm}$

Height, $h=10\text{cm}$
Converting to millimeters:
$h=10\times 10\text{mm}=100\text{mm}$

The formula for the total surface area of a solid cylinder is:
$A=2\pi r(r+h)$

Substitute the values of radius and height into the formula:
$A=2\times \pi \times 20\times (20+100)$
$A=40\times \pi \times 120$
$A=4800\pi {\text{mm}}^2$

Using the approximation $\pi \approx 3.14$:
$A\approx 4800\times 3.14$
$A\approx 15072{\text{mm}}^2$