Question

The T.S.A. of a cylinder is 462 cm^2. If C.S.A. is one-third of its T.S.A. .Find the volume of the cylinder.​

Answer 1

Solution :

TSA of the cylinder = 462 cm²

Given :

CSA of the cylinder = 1/3rd of its TSA

= ( 1 / 3 ) × 462 = 154 cm²

We know that

TSA of a cylinder = CSA of the cylinder + 2 × ( Area of base i.e circle )

Let the Area of the base i.e circle be x cm²

⇒ 462 = 154 + 2x

⇒ 462 - 154 = 2x

⇒ 308 = 2x

⇒ x = 308 / 2

⇒ x = 154

⇒ Area of base circle = 154 cm²

Let the base radius of the cylinder be ' r ' cm

⇒ πr² = 154 cm² --- EQ( 1 )

⇒ 22/7 × r² = 154

⇒ r² = 154 × 7 / 22

⇒ r² = 7²

⇒ r = 7

i.e Base radius of the cylinder ( r ) = 7 cm

Let the height of the cylinder be ' h ' m

CSA of the cylinder = 2πrh sq.units

⇒ 154 = 2 × 22/7 × 7 × h

⇒ 154 = 44h

⇒ h = 154 / 44

⇒ h = 7 / 2

i.e Height of the cylinder ( h ) = 7 / 2 cm

Volume of the cylinder = πr²h cu.units

From EQ( 1 )

= 154 × 7 / 2

= 539 cm³

Therefore the volume of the cylinder is 539 cm³.

Answer 2

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