Question

In a cylindrical vessel of radius 10cm, contain some water, 9000small spherical balls are dropped which completely emerge in water which Rises the water level if sperical ball is of radius 0.5 cm find the rise in a level of water in the vessel

Answer 1

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In a cylindrical vessel of radius 10 cm, contain some water, 9000 small spherical balls are dropped which completely emerge in water which rises the water level. if spherical ball is of radius 0.5 cm find the rise in the level of water in the vessel.

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Radius of cylindrical vessel, r = 10 cm

Let, rise of water = h cms

No. of spherical balls dropped = 9000

radius of spherical ball, s = 0.5 cm

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Volume of 9000 spherical balls =

$9000 \times \frac{4}{3} \pi {s}^{3} \\ \\ (puting \: values) \\ = 9000 \times \frac{4}{3} \times \pi \times {(0.5)}^{3} \\ \\ = 1500\pi \: \: {cm}^{3}$

Volume of water rise in the cylindrical vessel ( taking level of water rise equal h cms) =

$\pi {r}^{2} h \\ \\ ( putting \: values ) \\ = \pi \times {10}^{2} \times h \\ \\ = 100\pi \: h \: \: \: {cm}^{3}$

Volume of 9000 spherical balls will be equal to the volume of water rise in the vessel.

so,

1500 π = 100 π h

( π will be eliminated being on both sides)

1500 = 100 h

h = 15 cm

SO THERE WILL BE A RISE OF 15 CM IN THE LEVEL OF WATER.

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