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The length of a rectangular sheet of paper is 14 cm more than the width and the perimeter of the rectangular sheet is 116 cm. If this rectangular sheet of paper is rolled along its breadth to form a cylinder, then, the volume of the cylinder so formed is – 


1. 2350 cm3
2. 2168 cm3
3. 2200 cm3
4. 1386 cm3

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Correct Answer - Option 4 : 1386 cm3

Given:

Length of rectangular = Width + 14 cm = (b + 14) cm

Width of rectangular sheet = b

Formula used:

Perimeter of rectangle = 2(l + b)

Perimeter of circle = 2πr

Volume of cylinder = πr2h

Calculation:

According to question –

⇒ 2(b + b + 14) = 116

⇒ 2b + 14 = 58

⇒ 2b = 44

⇒ b = 22 cm

So, l = (22+ 14) cm = 36 cm, and b = 22 cm

Height of cylinder = length of sheet = L = 36 cm

Circumference of top = 2πr = Breadth of sheet = 22 cm

⇒ r = 22/2π = 22 × 7/44

⇒ 7/2

The volume of cylinder = πr2h

⇒ π(7/2)2× 36

⇒ (22 × 49/28) × 36

⇒ 22 × 7 × 9

⇒ 1386 cm3

∴ the volume of cylinder 1386 cm3

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