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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.


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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
    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

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  • Volume of iron= vol sphere = 4/3πr^2
    Volume of cylinder= πr^2h
    Vol of cylinder- vol of sphere