225) A hemispherical tank is made of steel 21cm thick. The inner radius of the tank is 35cm.
Find the volume of steel used in making the tank. (rt =)
22
Answers
The inner radius of the tank is 35 cm.
So, the inner radius of the hemispherical tank (r1) = 35 cm
Also, the hemispherical tank is made of steel 21 cm thick.
So, r2 = inner radius + outer radius = (35 + 21) cm = 56 cm
Now,
The volume of iron used = Volume of outer radius - Volume of inner radius
⇒ 2/3 π (r2)³ - 2/3 π (r1)³
⇒ 2/3 × 22/7 [(56)³ - (35)³]
⇒ 44/21 (175616 - 42875)
⇒ 44/21 (132741)
⇒ 44(6321)
⇒ 278124 cm³
To convert cm³ into m³ divide the value by 10^6
⇒ 0.27812 m³
Given :-
- Inner Radius = 35cm.
- Thickness of Stell = 21cm.
To Find :-
- Volume of Steel used in making The tank ?
Formula used :-
- Volume of Steel used = Outer Volume - Inner Volume = [(2/3) π * R³ ] - [(2/3) π * r³ ]
Solution :-
Given That,
→ Inner Radius = 35cm. = r
→ Outer Radius = inner Radius + Thickness = 35 + 21 = 56cm = R.
Putting Both Values we get :-
→ Volume = [(2/3) π * R³ ] - [(2/3) π * r³ ]
→ V = [(2/3) π * 56³ ] - [(2/3) π * 35³ ]
Taking (2/3) * π common,
→ V = (2/3) * π [ 56³ - 35³ ]
→ V = (2/3) * π [ 175616 - 42875 ]
→ V = (2/3) * (22/7) * 132741
→ V = (44 * 132741) / 21