**A steel ball of radius 1cm is dropped into a cylinder of radius 2cm and height 4...**

### Question

A steel ball of radius 1cm is dropped into a cylinder of radius 2cm and height 4cm. If the cylinder is now filled with water, what is the volume of the water in the cylinder?### Options

A) \(\frac{44\pi}{3}\) cm\(^3\)

B) \(12\pi\) cm\(^3\)

C) \(\frac{40\pi}{3}\) cm\(^3\)

D) \(32\pi\) cm\(^3\)

The correct answer is A.

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## Discussion (4)

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Volume of ball = Vsphere = 4πr³/3

= 4π1³/3= 4π/3

Volume of a cylinder= πr²h

=π2² (4) =16π

Volume of water = Vcylinder - V ball

= 16π - 4π/3 = 48π-4π/3= 44π/3

Answer is 44π/3

It should be noted that volume of a ball takes the volume of a sphere

Volume of a sphere = 4/3 πr³

Volume of a cylinder = πr²h

To calculate the volume of water in the cylinder;

Volume of cylinder - Volume of sphere

So we are calculating in terms of π;

( π × 2² × 4) - ( 4/3 × π × 1³ )

= 16π - 4/3π

= 44/3π.

Volume of a sphere is 4/3πr² and volume of a cylinder is πr²h putting in the values,

Volume of a sphere is 4/3π and Vol of cylinder is 16π

Subtract the volume of the sphere from the cylinder and you get optionA

Volume of iron= vol sphere = 4/3πr^2

Volume of cylinder= πr^2h

Vol of cylinder- vol of sphere