Question

A hollow garden roller 63 cm wide with a girth of 440 cm, is made of 4 cm thick iron. Find the volume of the iron.

Answer 1

Answer:

Step-by-step explanation:

Circumference of girth of roller = 440 cm

2*Pi*R = 440 = R (220*7/22) = 70 cm

Outer radius = 70 cm & inner radius = 70-4 cm = 66 cm

Therefore Volume or iron = Pi [(70^2 - 60^2)]*63

= 58752 cm^3

Answer 2

The volume of iron used in making the hollow garden roller is 1,07,712 cm³.

• Given data :

Width of the garden roller = 63 cm

Girth of the roller = 440 cm

Thickness of iron sheet used in the roller = 4 cm

• Girth means "circumference".

Therefore, circumference of the roller = 440 cm

A roller is cylindrical in shape.

∴  Circumference = 2πR, where R is the outer radius of the hollow roller.

=> 2πR = 440 cm

Or, 2 × (22 / 7) × R = 440 cm

Or, (2 × 22 × R) / 7

Or, 44R =  440 cm × 7

Or, R = (440 cm × 7) / 44

Or, R = 10 cm × 7

Or, R = 70 cm -(i)

• Thickness of iron sheet used in the hollow roller = Outer Radius - Inner Radius

• If the inner radius is taken as r, then thickness of the iron sheet used = R - r

Or, R - r = 4 cm

Or, 70 cm - r = 4 cm [ from eq. (i) ]

Or, 70 cm - 4 cm = r

Or, r = 66 cm

• We know that, volume of a hollow cylinder = Volume of outer cylinder - Volume of inner cylinder

Or, Volume of a hollow cylinder = πR²h - πr²h = πh (R² - r²)

Since a hollow roller is also a hollow cylinder, volume of the roller = πh (R² - r²)

• Now, height of the roller = width of the roller = 63 cm

∴  Volume of iron used in making the roller = Volume of the roller

Or, Volume of iron used in making the roller = πh (R² - r²)

= (22 / 7) × 63 cm × { (70 cm)² - (66 cm)² }

= 22 × 9 cm × (4900 cm² - 4356 cm²) × 9 cm  

[63 cm / 7 = 9]

= 22 × 9 cm × 544 cm²

= 1,07,712 cm³

∴ 1,07,712 cm³ is the volume of iron used in the roller.