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# 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.

## Discussion (4)

• 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

• 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