Question

A tank in the shape of a cylinder with a radius of 4m and a height of 7m is completely filled with water. If a metallic sphere of radius 3m is immersed into the tank and taken out, find the volume of water that remains in the tank.
1. 189.31 m³
2. 431.29 m³
3. 238.85 m³
4. 329.14 m³

Answer 1

Correct Answer - Option 3 : 238.85 m³

Given:

Radius of Tank (Cylinder) = 4m

Height of Tank (Cylinder) = 7m

Radius of Sphere = 3m

Concept: 

Volume of water removed = Volume of Sphere 

Formula used:

Volume of Cylinder = πr²h 

Volume of Sphere = (4/3)πr³  ; (where 'r' is the radius and 'h' is the height)

Calculation:

Volume of Cylinder = πr2h 

⇒ π × 4² × 7 = 112π

∴ Volume of Cylinder = 112π m³ 

Now, 

Volume of Sphere = (4/3)πr3  

⇒ (4/3) × π × (3³) = 36π 

Volume of Sphere = 36π m³

Volume of water removed = Volume of Sphere = 36π m³ 

Volume of water remains in the tank = Initial Volume of the tank - Volume of water removed

⇒ 112 π - 36 π = 76π 

Volume of water remains in the tank = 76π m³ 

⇒ 76 × (22/7) = 238.85 m3