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Deepak Bora
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A rectangular sheet of tin foil of size 30 cm × 18 cm can be rolled to form a cylinder in two ways along length and along breadth. Find the ratio of volumes of the two cylinders thus formed.

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This question is Based on Mensuration Chapter of M.L Aggarwal book for ICSE BOARD for class 10.
Here size of a rectangular sheet of tin foil is given.It can be rolled to form a cylinder in two ways along length and along breadth. Find the ratio of volumes of the two cylinders thus formed.
This is the Question Number 17, Exercise 17.1 of M.L Aggarwal.

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2 Answers

  1. This answer was edited.

    Given size of the sheet = 30 cm×18 cm

    If we roll it lengthwise, base circumference, 2πr = 30

    2×(22/7)r = 30

    r = 30×7/2×22 = 210/44 = 105/22 cm

    Height, h = 18 cm

    Volume of the cylinder, V1 = πr2h

    = (22/7)×(105/22)2×18

    = 15×105×9/11

    If we roll it breadthwise, base circumference, 2πr = 18

    2×(22/7)r = 18

    r = 18×7/2×22 = 126/44 = 63/22 cm

    Height, h = 30 cm

    Volume of the cylinder, V2 = πr2h

    = (22/7)×(63/22)2×30

    = 9×63×15/11

    V1/V2 = (15×105×9/11)÷( 9×63×15/11)

    = (15×105×9/11)×(11/9×63×15)

    = 105/63

    = 15/9

    = 5/3

    Ratio of the volumes of two cylinders is 5:3.

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  2. This answer was edited.

    I hope this helps!!!!!

    Q.

    A rectangular sheet of tin foil of size 30 cm × 18 cm can be rolled to form a cylinder in two ways along length and along breadth. Find the ratio of volumes of the two cylinders thus formed.

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