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150 spherical marbles,each of diameter 1.4 …

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150 spherical marbles,each of diameter 1.4 cm,are dropped in a cylindrical vessel of diameter 7cm containing some water, which are completely immersed in water. Find the rise in water in the vessel.

Posted by Sumit Kumar 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Diameter of spherical marble = 1.4 cm

Radius {tex}r _ { 1 } = 1.4 / 2 = 0.7 = 7 / 10 \mathrm { cm }{/tex}

Diameter of cylindrical vessel = 7 cm

Radius R = 7/2 cm

Let h be the rise m water level then

Volume of 150 spherical marbles = volume of water rises

or, {tex}150 \times \frac { 4 } { 3 } \times \pi \times \frac { 7 } { 10 } \times \frac { 7 } { 10 } \times \frac { 7 } { 10 } = \pi \times \frac { 7 } { 2 } \times \frac { 7 } { 2 } \times h{/tex}

or, {tex}h = \frac { 4 \times 7 } { 5 }{/tex}

or, {tex}\frac { 28 } { 5 } = h{/tex}

or, h = 5.6 cm

The rise is the level of water, h = 5.6 cm

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