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The capacity of a closed cylindrical vessel of height 1 m is 15.4 L. How many square metres of metal sheet would be needed to make it?

Solution:

The volume of the cylinder = 15.4 litres

1 litre = 1000cm³

1 litre = 1000/1000000 m³

1 litre = 1/1000 m³ = 0.001 m³

Volume of cylinder = πr²h

h = 1m

r = ?

πr²h = 15.4 × 0.001 m³

(22/7) × r² × (1) = 15.4 × 0.001 m³

r² = (15.4/22) × 7 × 0.001 m²

r² = 0.7 × 7 × 0.001m²

r² = 7 × 7 × 0.0001m²

r = 7 × 0.01 m = 0.07m

The area of the metal sheet required for making of this closed cylinder will be = 2πrh

= 2 × 22/7 × 0.07 × 1

= 0.44m²

Hence 0.44m² of metal sheet is required to make the cylinder.

✦ Try This: The capacity of a closed cylindrical vessel of height 2 m is 30.8 L. How many square metres of metal sheet would be needed to make it?

The volume of the cylinder = 30.8 litres

1 litre = 1000cm³

1 litre = 1000/1000000 m³

1 litre = 1/1000 m³ = 0.001 m³

Volume of cylinder = πr²h

h = 2m

r = ?

πr²h = 30.8 × 0.001 m³

(22/7) × r² × (2) = 30.8 × 0.001 m³

r² = (30.8/22) × 1/2 × 7 × 0.001 m²

r² = (15.4/22) × 7 × 0.001m²

r² = 0.7 × 7 × 0.001m²

r² = 7 × 7 × 0.0001m²

r = 7 × 0.01 m = 0.07m

The area of the metal sheet required for making of this closed cylinder will be = 2πrh

= 2 × 22/7 × 0.07 × 1

= 0.44m²

Hence 0.44m² of metal sheet is required to make the cylinder.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Problem 110

The capacity of a closed cylindrical vessel of height 1 m is 15.4 L. How many square metres of metal sheet would be needed to make it?

Summary:

The capacity of a closed cylindrical vessel of height 1 m is 15.4 L. 0.44 square metres of metal sheet would be needed to make it

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