Question

a hollow garden roller if 42 cm diameter and length 147 cm is made of cast iron of 2cm thickness. the volume of the iron used in the roller​

Answer 1

Given data :-

• A hollow garden roller if 42 cm diameter and length 147 cm is made of cast iron of 2cm thickness.

Here,

→ Diameter of roller ( d ) = 42 cm

→ Height of roller ( h ) = 147 cm

→ Thickness of iron ( t ) = 2 cm

Solution :-

To find the volume of the iron used in the roller .

{From given}

→ Radius of roller ( R ) = ½ × d

→ Radius of roller ( R ) = ½ × 42

→ Radius of roller ( R ) = 21 cm

Here, radius of roller without thickness of iron {which is used in roller}.

→ radius of roller ( r ) = R - t

→ radius of roller ( r ) = 21 - 2

→ radius of roller ( r ) = 19 cm

Now we use formula to find volume of the iron used in the roller.

→ Volume of iron = π [ R² - r² ] h

→ Volume of iron = 22/7 [ (21)² - (19)² ] 147

→ Volume of iron = 22/7 [ 441 - 361 ] 147

→ Volume of iron = 22/7 × 80 × 147

→ Volume of iron = 1760/7 × 147

→ Volume of iron = 258720/7

→ Volume of iron = 36960 cm³

Hence, the volume of the iron used in the roller is 36960 cm³.

Answer 2

Given :

1. Diameter ( D ) = 42 cm
2. Length ( L ) = 147 cm
3. Thickness ( T ) = 2 cm

To find :

The volume of the Iron used in the roller

Solution :

Radius using diameter :

Radius 1 = ½ × D

= ½ × 42

= 21 cm

Radius with thickness :

Radius 2 = R - T

= 21 - 2

= 19 cm.

Volume = π ( R1² - R2² ) L

= 22 / 7 ( 21² - 19² ) 147

= ( 22 / 7 ) × ( 441 - 361 ) × ( 147 )

= 1760 / 7 × 147

= 258720 / 7

= 36960 cm.

Hence, Volume = 36960 cm