Question

A solid cylinder has a total surface area of 462 cm². It's curved surface area is one-third of it's total surface area. Find the radius and height of the cylinder.​

Answer 1

Answer:

r= 7 cm,h=7/2 cm

Step-by-step explanation:

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

Then, total surface area of cylinder = 2πr (r + h)

Curved surface area of cylinder = 2πrh 

We have, 

Curved surface area = 1/3(Total surface area) = 1/3 x 462 cm2 = 154 cm2 

⇒  2πrh = 154 

Also, 2πrh + 2πr2 = 462    ⇒ 154 + 2πr2 = 462

⇒  2πr2 = 462 - 154 = 308 cm2

2 x 22/7 x r2 = 308

⇒  r2 = 308 x 7/2 x 22 = 72  ⇒  r = 7 cm

Again 2πrh = 154    ⇒ 2 x 22/7 x 7 x h = 154 

⇒ h = 154/2 x 22 = 7/2 cm 

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