 # Formula of Curved Surface Area Cylinder

A cylinder is a three-dimensional solid, whose circular base and 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- The area of a cylinder is defined as the 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