Question

Please someone answer this:


The diameter of the circular base and the height of a right cylinder are equal.The cylinder is filled with water to the brim. Four equal solid spherical balls are put into it. The diameter of each sphere is equal to the radius of the base of the cylinder. what percentage of water will flow out.

Answer 1

» The diameter of the circular base and the height of a right cylinder are equal.

Diameter of cylinder = Height of cylinder

Let diameter of cylinder = M

So height of cylinder also = M

Radius of cylinder = M/2

» Four equal solid spherical balls are put into it.

Radius of each ball = M/4

• We have to find the percentage of water that flows out.

i.e.

=> Volume of cylinder - 4(Volume of each ball)

=> πr²h - 4(4/3πr³)

=> π(M/2)² M - 16/3 π (M/4)³

=> π [(M³/4) - 16/3 (M³/64)

=> π (M³/4 - M³/12)

=> 22/7 × M³/6

=> 0.524 M³

Now ..

Percentage of water that flows through it

=> $\dfrac{0.524 {M}^{3} }{ \frac{\pi {M}^{3} }{4} }$ × 100

=> (0.524 × 4 × 7 × 100)/22

=> 0.666 × 100

=> 66.6 %

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66.6% of the water will flow out.

___________ [ ANSWER ]

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Answer 2

Diameter & height of cylinder are equal

Let diameter of cylinder = x

Then, height of cylinder also = x

Radius of cylinder = x/2

Radius of 4 ball = x/4

According to Question;

Volume of cylinder - 4(Volume of each ball)

πr²h - 4(4/3πr³)

π(x/2)² x - 16/3 π (x/4)³

π [(x³/4) - 16/3 (x³/64)

π (x³/4 - x³/12)

22/7 × x³/6

0.524 x³

Percentage of water that flows

0.54x³/πx³/4 × 10

(0.524 × 4 × 7 × 100)/22

0.666 × 100

66.6 %