A cylinder is cut lengthwise and flattened thereby forming a rectangle of dimension 66cmx28cm. Find the curved surface area and volume of the original cylinder.
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We know that the curved surface area of a right circular cylinder with radius r and height h is CSA=2πrh.
It is given that the length of the rectangular sheet is l=44 cm and the height of the sheet is h=20 cm. Since the cylinder is formed among the length, therefore, length of rectangular sheet is equal to circumference of base that is:
l=2πr⇒44=2×722×r⇒r=2×2244×7=7
Therefore, the radius of the rectangular sheet is 7 cm.
We also know that the volume of a right circular cylinder with radius r and height h is V=πr2h.
Here, the height is h=20 cm and the radius is r=7 cm, therefore,
V=πr2h=722×(7)2×20=722×49×20=3080 cm3
Hence, the volume of the cylinder is 3080 cm3.
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