If the height of a solid right circular cylinder is 27 cm and diameter of its base is 30 cm, the total surface area (in cm²) of the right circular cylinder is:

Take $\pi =\frac{22}{7}$

The correct option is 3960.

Given Data:

Height of the cylinder (h) = 27 cm
Diameter of the base (d) = 30 cm

Step 1: Find the radius of the base

The radius (r) is half of the diameter:

$r=\frac{30}{2}=15\text{ cm}$

Step 2: Formula for the total surface area of a right circular cylinder

The total surface area (TSA) of a solid cylinder is given by:

$\text{TSA}=2\pi r(h+r)$

Step 3: Substitute the given values into the formula

Using $\pi =\frac{22}{7}$:

$\text{TSA}=2\times \frac{22}{7}\times 15\times (27+15)$

$\text{TSA}=2\times \frac{22}{7}\times 15\times 42$

Step 4: Simplify the expression

Dividing 42 by 7 gives 6:

$\text{TSA}=2\times 22\times 15\times 6$

$\text{TSA}=44\times 90$

$\text{TSA}=3960\text{ cm}{}^2$

Thus, the total surface area of the right circular cylinder is 3960 cm².