Q5 of 79 Page 229

The total surface area of a solid right circular cylinder is 231 cm2. Its curved surface area is two thirds of the total surface area. Find the radius and height of the cylinder.

Given : TSA of cylinder = 231 cm2

CSA of cylinder = TSA of cylinder = × 231 = 154 cm2


To find : Radius of cylinder = r = ?


Height of cylinder = h = ?


Formula : CSA of cylinder = 2πrh


TSA of cylinder = 2πr (h + r)


Solution : CSA of cylinder = 2πrh


⇒ 2 × × r × h = 154


r × h = = 24.5 (1)


TSA of cylinder = 2r (h + r)


⇒ 2rh + 2r2 = 231


154 + 2r2 = 231


⇒ 2r2 = 231 – 154 = 77


2 × × r2 = 77


⇒ r2 = =


⇒ r = = 3.5 cm


From (1),


r × h = 24.5


⇒ 3.5 × h = 24.5


⇒ h =


h = 7 cm


∴ The radius and height of the right circular cylinder is 3.5 cm and 7 cm respectively.


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