A rectangular sheet of paper 40 cm × 22 cm, is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is

Given: Dimensions of rectangular sheet: 40cm × 22cm


Height of the Hollow Cylinder : 40cm


Area of the Rectangle is = length × breadth


Curved surface Area of the Cylinder = 2πrh (where r and h are radius and height of cylinder respectively)


Let a1 be the area of Rectangle


a1 = 40 × 22 cm2


Let a2 be the Curved surface area of Cylinder


a2 = 2 × π × r × 40 cm2


We know that when area of a surface doesn’t change even if its shape is changed.


a1 = a2


40 × 22 = 2 × π × r × 40


r = = = = = 3.5 cm


Radius of the Cylinder is 3.5cm

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