A solid cylinder has total surface area of 462 cm square. -Maths 9th

A solid cylinder has total surface area of 462 cm square. -Maths 9th
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Let r cm be the radius of the base and h cm be the height of the cylinder, Then, total surface area of cylinder = 2 πr (r + h) Curved surface area of cylinder = 2 πrh  We have,  Curved surface area = 1/3(Total surface area) = 1/3 x 462 cm2 = 154 cm2  ⇒  2 πrh = 154  Also, 2 πrh + 2 πr2 = 462    ⇒ 154 + 2 πr2 = 462 ⇒  2 πr2 = 462 - 154 = 308 cm2 2 x 22/7 x r2 = 308 ⇒  r2 = 308 x 7/2 x 22 = 72  ⇒  r = 7 cm Again 2 πrh = 154     ⇒ 2 x 22/7 x 7 x h = 154  ⇒ h = 154/2 x 22 = 7/2 cm  Volume of the cylinder =  πr2h = 22/7 x 7 x 7 x 7/2 = 539 cm3
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