## Cylinder-Geometry Formulas

### Cylinder

A cylinder is a three-dimensional shape with two round shapes at either end and two parallel lines connecting the round ends. Bases are always parallel and congruent to each other.

### Volume of Cylinder:

Volume of Cylinder is defined as the total space occupied by the cylinder. The volume is denoted as “V”. It is measured in terms of cubic units.

Volume V= πr2h

### Example:

find the volume of a cylinder that has the radius 3 cm and height 5 cm.

V = π ( 3²) 5

= π ( 9 ) 5

= (3. 14) (45)

= 141.30 cm³

### Curved Surface Area of Cylinder:

Curved Surface Area is the area of all the curved regions

Curved surface Area= 2πrh

### Example:

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

### Solution:

C.S.A. = 2πrh = 2π × 1 × 5 = 10π

### Total surface Area of Cylinder:

Total Surface Area is the area of all the surfaces including the base of a 3D object

Total surface Area= 2πr( r + h )

### Example:

Find the total surface area of the cylinder, whose radius is 5cm and height is 10cm?

### Solution:

T.S.A = 2π × 5(5 + 10)

= 2π × 5(15)

= 2π × 75

= 150 × 3.14

= 471 cm2

### Properties of Cylinder:

• A cylinder has only one curved side.
• A cylinder has two identical flat ends that are circular or elliptical.
• The bases are always congruent and parallel.
• It is similar to the prism since it has the same cross-section everywhere.