**Curved Surface Area and Total Surface Area of Cylinder Examples :**

Here we are going to see, some example problems of finding 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) |

**Question 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

x^{2} = 5500 (7/22) ⋅ (1/2) ⋅ (1/35)

x^{2} = 25

x = 5

Radius = 5(5) = 25 cm

Height = 7(5) = 35 cm

**Question 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 + 2Πr^{2} = 1848

1540 + 2Πr^{2} = 1848

2Πr^{2} = 1848 - 1540

2(22/7)r^{2} = 308

r^{2} = 308 (7/22)(1/2)

r^{2} = 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

**Question 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 cm^{2 }

After having gone through the stuff given above, we hope that the students would have understood, "Curved Surface Area and Total Surface Area of Cylinder Examples".

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