Q8 of 67 Page 190

The volume and curved surface area of a cylinder are 1650 cm3 and 660 cm2 respectively. Find the radius and the height of the cylinder.

Let r be the radius of base and h be the height of cylinder


Curved surface area of cylinder = 660 cm2


Curved surface area = 2πrh


⇒ 2πrh = 660


⇒ 2 × × r × h = 660


⇒ r × h =


⇒ r × h =


⇒ r × h = 15 × 7


⇒ r × h = 105


⇒ rh = 105


Volume of cylinder = 1650 cm3


Volume of cylinder = πr2h


⇒ πr2h = 1650


⇒ × r × r × h = 1650


Using r × h = 105 we get


⇒ × r × 105 = 1650


⇒ 22 × 15 × r = 1650


⇒ r =


⇒ r =


⇒ r = 5 cm


Substitute r = 5 in r × h = 105 to get h


⇒ 5 × h = 105


⇒ h =


⇒ h = 21 cm


Therefore, radius is 5 cm and height is 21 cm


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