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The curved surface area of a cylinder is 4400 cm² and the circumference of its base is 110 cm. Then, the volume of the cylinder is ____.

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Detailed Solution

The curved surface area of a cylinder is 4400 cm² and the circumference of its base is 110 cm. Then, the volume of the cylinder is

38500 c m 3

.
Given that the curved surface area of cylinder

= 4400cm 2

.
Circumference of base of cylinder

= 110 c m

.
We know that curved surface area of cylinder

= 2 π r h

4400 = 2 π r h

…………… (1)
Circumference of circle

= 2 π r

110 = 2 π r

…………… (2)
Substituting the value of

2 π r

from equation (2) in equation (1),

4400 = 110 × h

h = 4400110

h = 40 c m

Substituting

h = 40 c m

in equation (1),

4400 = 2 π r (40)

4400 = 2 × 227 r (40)

4400 = 17607 r

r = 4400 × 71760

r = 308001760

r = 17.5 c m

Volume of cylinder,

V = π r 2 h

.
Substituting the value of r and h in above equation,

V = 227 × 17.5 × 17.5 × 40

V = 227 × 306.25 × 40

V = 227 × 12250

V = 2695007

V = 38500 c m 3

Therefore, the volume of the cylinder is

38500 c m 3

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