Question

A sold cylinder has T.S.A = 462 sq.cm its curved surface area is 1/3 of its T.S.A find the volume of cylinder ​

Answer 1

TSA of the cylinder = 462 cm²

Given : $\sf$

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 --- equ( 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 equ( 1 )

= 154 × 7 / 2

= 539 cm³

Therefore the volume of the cylinder is 539 cm³.

Answer 2

GIVEN:-

• Total Surface area of Cylinder is 462sq.cm

• Curved surface area is 1/3 of T.S.A

TO FIND:-

• The Volume of Cylinder.

FORMULAE USED

• ${\boxed{\rm{T.S.A=2\pi r(r+h) or 2\pi r^2+2\pi rh}}}$..........1

• ${\boxed{\rm{\pi r^2h}}}$

Now,

atq.

Curved surface area = 1/3 of total Surface area.

Curved surface area =$\rm{\dfrac{1}{3}\times{462}}$

Curved surface area= 154sqcm²

2πrh= 154sq.cm²........2

Now out the value of eq 2 in eq.1

$\implies\rm{2\pi rh+2\pi r^2=462}$

$\implies\rm{2\pi r^2=462-154}$

$\implies\rm{2\pi r^2=308sq.cm^2}$

$\implies\rm{r^2=\dfrac{308}{2\pi}}$

$\implies\rm{r^2=\sqrt{49}}$

$\implies\rm{r=7cm}$

Substitutimg the value of r in eq.2

$\implies\rm{2\pi rh=154sq.cm^2}$

$\implies\rm{2\pi h=\dfrac{154}{7}}$

$\implies\rm{h=\dfrac{7}{2}}$

Now,

$\implies\rm{Volume\:of\: Cylinder=\pi r^2h}$

$\implies\rm{Volume\:of\: Cylinder=\dfrac{22}{7}\times{49}\times{\dfrac{7}{2}}}$

$\implies\rm{Volume\:of\: Cylinder=539cm^3}$