Question

If the radius and height of a right cylinder are in the ratio 1:3 and total surface area is 1232cm², find its volume.​

Answer 1

Given :-

• The radius and height ratio = 1 : 3
• The T.S.A of cylinder = 1232 cm²

To Find :-

• The volume of Cylinder = ?

Solution :-

• To calculate the volume of Cylinder at first we have to find out the radius and the height of cylinder then calculate the volume of Cylinder.

Calculate begins :-

• Let, radius be X , height be 3X

⇢ T.S.A of Cylinder = 2 × π × h × r + 2 × π ×r²

⇢ T.S.A of Cylinder = 2 π r( h + r)

• Putting above values we get :-

⇢ 2 × 22/7 × X(3X + X) = 1232

⇢ 2 × 22/7 × X(4X) = 1232

⇢ 44 × 4X² = 1232 × 7

⇢ 4X² = 28 × 7

⇢ X² = 7 × 7

⇢ X = √49

⇢ X = 7 cm

Now, we have here :-

• Height (3X) = 3 × 7 = 21 cm
• Radius (X) = 7 × 1 = 7 cm

⇢ Volume of Cylinder = π × r² × h

⇢ Volume = 22/7 × 7² × 21

⇢ Volume = 22/7 × 7 × 7 × 21

⇢ Volume = 22 × 7 × 21

⇢ Volume = 3234 cm³

Hence,

• The volume of Cylinder = 3234 cm³

Answer 2

Answer:

Given :-

• Radius : Height= 1 : 3

• Total Surface Area = 1232 cm²-------- eq 1

Need To Find :-

• Volume = ?

Solution :-

Let, radius be R then height will be 3R,----2

we know,

Total Surface Area of Cylinder = 2 πr( h + r)

From eq 1,

2 × 3.14× R(3R + R) = 1232

2 × 3.14 × R(4R) = 1232

44 × 4R² = 1232 × 7

4R² = 28 × 7

R² = 7 × 7

R= 7 cm

Substituting value of X in equation 2 we get,

Radius= 7 × 1 = 7 cm

Height = 3 × 7 = 21 cm

Now,

Volume of Cylinder = πr²h

Volume = 3.14 × 7² × 21cm³

Volume = 3.14 × 7 × 7 × 21cm³  

$\red{\boxed{ Volume = 3234 cm³}}$