CURVED SURFACE AREA AND TOTAL SURFACE AREA OF CYLINDER EXAMPLES

Formula for Curved Surface Area and Total Surface Area of Cylinder

	Curved surface area  =  2Πrh Total surface area of  =  2Πr(h + r)
	Curved surface area    =  2Π(R + r)h Total surface area    =  2Π(R + r)(R - r + h)

Example 1 :

The radius and height of a cylinder are in the ratio 5:7 and its curved surface area is 5500 sq.cm. Find its radius and height.

Solution :

Radius of cylinder (r)  =  5x

Height of cylinder (h)  =  7x

Curved surface area of cylinder  =  5500 sq.cm

 2Πrh  =  5500

2⋅(22/7) ⋅ 5x ⋅ 7x  =  5500

x²  =  5500 (7/22) ⋅ (1/2) ⋅ (1/35)

x²  =  25

x  =  5

Radius  =  5(5)  =  25 cm

Height  =  7(5)  =  35 cm

Example 2 :

A solid iron cylinder has total surface area of 1848 sq.m. Its curved surface area is five – sixth of its total surface area. Find the radius and height of the iron cylinder.

Solution :

Total surface area of cylinder  =  1848 sq.cm

curved surface area  =  (5/6) of 1848

  =  (5/6) 1848

 2Πrh  =  1540----(1)

 2Πr(h + r)  =  1848

 2Πrh + 2Πr²  =  1848

1540 + 2Πr²  =  1848

2Πr²  =  1848 - 1540

2(22/7)r²  =  308

r²  = 308 (7/22)(1/2)

r²  =  49

r  =  7 m

By applying the value of r in (1), we get 

 2 ⋅ (22/7) ⋅ 7 h  =  1540

h  =  1540/44

 h  = 35 m

Example 3 :

The external radius and the length of a hollow wooden log are 16 cm and 13 cm respectively. If its thickness is 4 cm then find its T.S.A.

Solution :

External radius (R)  =  16 cm

height of log  =  13 cm

thickness  =  4 cm

thickness =  R - r ==>  4  =  16 - r

Internal radius (r)  =  16 - 4  =  12 cm

Total surface area  =  2Π(R + r) (R - r + h)

  =  2 ⋅ (22/7) (16 + 12) (16 - 12 + 13)

  =  2 ⋅ (22/7) (28) (17)

  =  2992 cm² 

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