## CURVED SURFACE AREA OF CYLINDER

Curved surface area of cylinder is the measurement of outer area,  where the extension of top and bottom portion wont be included.

## Curved surface area of cylinder If a rectangle revolves about one side and completes one full rotation, the solid thus formed is called a right circular cylinder. The above picture shows that how rectangle forms a right circular cylinder. In other words curved surface area is simply said as CSA

CSA of cylinder = 2 π r h

"r" and "h" stands for radius and height of cylinder.

## Curved surface area of hollow cylinder

A hollow cylinder is a three dimensional solid bounded by two parallel cylindrical surfaces and by two parallel circular bases cut out from two parallel planes by these two cylindrical surfaces. CSA of hollow cylinder = 2πh(R+r)

R  =  external radius, r = internal radius and h  =  height

## Example problems of curved surface area of cylinder

Example 1 :

A solid right circular cylinder has radius of 14 cm and height of 8 cm. Find its CSA.

Solution : Radius of the cylinder (r)  =  14 cm

Height of the cylinder (h)  =  8 cm

Curved surface area of cylinder  =  2Πrh

=  2 (22/7)  14 ⋅  8

=  704 sq.cm

Curved surface area of cylinder  =  704 sq.cm

So, curved surface area of cylinder is 704 sq.cm

Example 2 :

Curved surface area and circumference at the base of a solid right circular cylinder are 4400 sq.cm and 110 cm respectively. Find its height and diameter.

Solution :

CSA of cylinder  =  4400 sq.cm

Circumference of the base  =  110 cm

2Πr  =  110 ==> 2 ⋅ (22/7) ⋅ r  =  110

r  =  110  (1/2) ⋅ (7/22)

r  =  17.5 cm

diameter  =  2r  =  2(17.5)

diameter  =  35 cm

2 Π r h   =   4400

110  h  =  4400

h  =  4400/110

h  =  40 cm

Height  =  40 cm

Diameter of the cylinder  =  35 cm

So, height and diameter of cylinder is 40 cm and 35 cm respectively.

Example 3 :

A mansion has 12 right cylindrical pillars each having radius 50 cm and height 3.5 m. Find the cost to paint the curved surface of pillars at \$ 20 per square meter.

Solution :

The pillars of the mansion are in the shape of cylinder

Radius = 50 cm ==>  0.5 m

Height = 3.5 m

CSA of one pillar   =  2 ⋅ (22/7) ⋅ 0.5 ⋅ 3.5

=   2 ⋅ 22  0.5 ⋅ 0.5 ==> 11 m2

CSA of 12 pillars  =  12 ⋅ 11

=  132 m2

Cost to paint per m2  =  \$ 20

Total cost  =  20  132

=  \$ 2640

Hence, total cost of painting 12 pillars is \$ 2640

Example 4 :

The total surface area of a solid right circular cylinder are 231 cm². Its curved surface area is two thirds of the total surface area. Find the curved surface area if cylinder.

Solution :

Curved surface area = (2/3)  Total surface area

2 Π r h  =  (2/3) ⋅ 231

2 Π r h  =  2 ⋅ 77

2 Π r h  =  154

Hence, curved surface area of cylinder is 154 cm2

Example 5 :

The total surface area of a solid right circular cylinder is 1540 cm². If the height is four times the radius of the base, then find the CSA of cylinder.

Solution :

Total surface area of cylinder  =  1540 cm²

CSA of cylinder + top area + bottom area = 1540 cm²

2 Π r (h + r)  =  1540

h  =  4 ⋅ radius of the base

h  =  4 r

2 Π r (4r+r)  =  1540

2 Π r (5r)  =  1540

2 ⋅ (22/7) ⋅ 5 r2  =  1540

=  1540 ⋅ (1/2) ⋅  (7/22) ⋅ (1/5)

=  (1540 ⋅ 7)/(2 ⋅ 22 ⋅ 5)

=  (1540 ⋅ 7 )/(2 ⋅ 22 ⋅ 5)

r2  =  49

r  =   √(77)

r  =  7 cm

Curved surface area of cylinder :

=  1540 -  (22/7) ⋅ ⋅ 7

=  1540 - 308

=  1232 cm2

Hence, CSA of cylinder  =  1232 cm2. Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

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