# Formula of Curved Surface Area Cylinder

A cylinder is a three-dimensional solid, whose circular base & top are parallel to each other. The perpendicular distance between the top and the base is defined as the total height of the cylinder.

Area of a cylinder- Area of a cylinder is defined as space or region occupied by the cylinder. This area can be of two types:

Curved Surface Area- The curved surface area is defined as the area of only curved surface, leaving the circular top and base.

Total Surface Area- It is the area of the curved surface as well as the bases.

Formula for calculating the Curved Surface Area (C.S.A.)-

Consider a cylinder having a height ‘h’ and base radius ‘r’.

The curved surface area of a cylinder is given as-

C.S.A.= $2\pi r h$

Example- Consider a curved surface area of a cylinder having height of 5 cm and diameter of base to be 2 cm.

Solution- Given h = 5 cm, and d = 2 cm,

thus r = 1 cm

C.S.A. = $2\pi r h = 2 \pi \times 1 \times 5 =10 \pi$

Example- Given the C.S.A. of a cylinder to be $154 cm^{2}$, and the height to be equal to twice the radius of the base. Find the radius and height of a cylinder.

Solution- Given C.S.A. = $154 cm^{2}$

$h = 2r$
$2 \pi \times r \times h = 154$

Putting the value of h=2r, we have

$\Rightarrow 2 \times \frac{22}{7} \times r \times (2r) = 154$
$\Rightarrow r^{2} = \frac{49}{4}$
$\Rightarrow r = \frac{7}{2}$

$\Rightarrow r = 3.5$cm

And h = 2r = 7cm

Thus h = 7 cm and r = 3.5 cm