If the radius and height of a right circular cylinder are 21 cm and 5 cm, respectively, then the total surface area of the cylinder is use $\pi =\frac{22}{7}$

The correct option is 3432 cm².

To find the total surface area of a right circular cylinder, we use the standard surface area formula:
$A=2\pi r(r+h)$
where:
• $r$ is the radius of the cylinder's base,
• $h$ is the height of the cylinder, and
• $\pi$ is approximately $\frac{22}{7}$.

From the given problem, we have:
Radius ($r$) = 21 cm
Height ($h$) = 5 cm

Substitute these values into the formula:
$A=2\times \frac{22}{7}\times 21\times (21+5)$

Simplify the expression step-by-step:
First, sum the values inside the parentheses:
$21+5=26$

Next, substitute this sum back into the formula and simplify the division:
$A=2\times \frac{22}{7}\times 21\times 26$
Since $\frac{21}{7}=3$, we can write:
$A=2\times 22\times 3\times 26$

Now, perform the multiplication:
$A=44\times 78$
$A=3432{\mathrm{cm}}^2$

Therefore, the total surface area of the cylinder is 3432 cm².