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A hollow garden roller of 42 cm diameter and length 152 cm is made of cast iron 2 cm thick. Find the volume of iron used in the roller.

Solution:

A hollow garden roller is in the form of concentric cylinders.

The diameter of the garden roller is 42 cm and which is basically the inner diameter.

The Diameter of the inner cylinder = 42 + (2 + 2) = 46cm

The Volume of Outer cylinder is = πR²h

The Volume of the inner cylinder is = πr²h

R = 46/2 = 23 cm

r = 42/2 = 21 cm

The Volume of the outer cylinder is = π × (23)² × 152

The Volume of the inner cylinder = π × (21)² × 152

The Volume of Iron used in the roller = [π × (23)² × 152] - [π × (21)² × 152]

= π × 152 × [(23)² - 21²]

= π × 152 × [23 + 21][23 - 21]

= π × 152 × 44 × 2

= 42,038.86cm³

✦ Try This: A hollow garden roller of 38 cm diameter and length 160 cm is made of cast iron 2 cm thick. Find the volume of iron used in the roller.

A hollow garden roller is in the form of concentric cylinders.

The diameter of the garden roller is 38 cm and which is basically the inner diameter.

The Diameter of the inner cylinder = 38 + (2 + 2) = 42cm

The Volume of Outer cylinder is = πR²h

The Volume of the inner cylinder is = πr²h

R = 42/2 = 21 cm

r = 38/2 = 19 cm

The Volume of the outer cylinder is = π × (21)² × 160

The Volume of the inner cylinder = π × (19)² × 160

The Volume of Iron used in the roller = [π × (21)² × 160] - [π × (19)² × 152]

= π × 160 × [(21)² - (19)²]

= π × 160 × [21 + 19][21 - 19]

= π × 160 × 40 × 2

= 40,228.57cm³

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

NCERT Exemplar Class 8 Maths Chapter 11 Problem 102

A hollow garden roller of 42 cm diameter and length 152 cm is made of cast iron 2 cm thick. Find the volume of iron used in the roller.

Summary:

A hollow garden roller of 42 cm diameter and length 152 cm is made of cast iron

2 cm thick. The volume of iron used in the roller.is 42,038.86cm³

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