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A rectangular paper 22 cm long and 14 cm wide is rolled along its width to form a cylinder. Find the curved surface area of the cylinder formed.
308 sq cm
154 sq cm
462 sq cm
616 sq cm
308 sq cm
When a rectangular sheet is rolled to form a cylinder, the curved surface area of the cylinder is exactly equal to the area of the rectangle used to form it. Simply multiply 22├Ч14=308.
Length of the rectangular paper = 22 cm, width of the rectangular paper = 14 cm.
CSA=Area┬аof┬аRectangle=L├ЧW
When a rectangular sheet is rolled to form a cylinder, the curved surface area of the cylinder is exactly equal to the area of the rectangle used to form it. Simply multiply 22├Ч14=308.
Students often waste time calculating the radius of the base using 2╧Аr=22 and then applying 2╧Аrh, which is unnecessary as the area remains conserved.
Analyze the transformation
When a rectangle is rolled along one side to form a cylinder, the paper becomes the lateral surface of the cylinder. Therefore, the curved surface area (CSA) is equal to the area of the rectangle.
CSA=L├ЧW
Substitute the given values
Given that the length L=22┬аcm and width W=14┬аcm, substitute these values into the area formula.
CSA=22┬аcm├Ч14┬аcm
Calculate the final result
Perform the multiplication to find the total surface area.
CSA=308┬аsq┬аcm
A is correct because the area of the rectangle used to form the cylinder is 22├Ч14=308┬аsq┬аcm, which equals the curved surface area.
This concept of area conservation also applies to sectors of a circle rolled into cones; understanding that surface areas match helps solve complex geometry problems quickly.