Question

A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm partly filled with water. If the sphere is completely submerged then the water level rises ​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Diameter of sphere = 18 cm

$\:\:$

• Sphere is dropped in cylindrical vessel partly filled with water

$\:\:$

• Diameter of cylindrical vessel = 36 cm

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$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• If the sphere is completely submerged then the water level rises

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

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• Diameter of sphere = 18 cm

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Radius of sphere = $\sf \dfrac { Diameter } { 2 }$

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➨ Radius = 9 cm

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$\underline{\bold{\texttt{Volume of sphere :}}}$

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➠ $\sf \dfrac { 4 } { 3 } \pi r^3$

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• r = Radius of sphere

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➜ $\sf \dfrac { 4 } { 3 } \pi 9^3$

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➜ $\sf \dfrac { 4 } { \cancel 3 } \pi \times \cancel 9 \times 9 \times 9$

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➜ $\sf 4 \times \pi \times 3 \times 9 \times 9$

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➨ 972π cm³ ------ (1)

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• Diameter of cylindrical vessel = 36 cm

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Radius of cylindrical vessel = $\sf \dfrac { Diameter } { 2 }$

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➨ Radius = 18 cm

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$\underline{\bold{\texttt{Volume of cylindrical vessel :}}}$

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➠ πR²h

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• R = Radius of cylindrical vessel

• h = Height of water raised when sphere is dropped

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➨ π18²h cm³ ------- (2)

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Now ,

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Volume of water rise = Volume of sphere

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〚 As water will rise in the cylindrical vessel only hence the volume of water rise can be calculated by volume of cylindrical vessel 〛

$\:\:$

$\underline{\bold{\texttt{Thus , (1) = (2)}}}$

$\:\:$

➜ 972π = π18²h

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➜ 972 = 18²h

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➜ $\sf h = \dfrac { 972 } { 18 \times 18 }$

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➜ $\sf h = \dfrac { 54 } { 18 }$

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➨ h = 3 cm

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Hence the water in cylindrical vessel will rise upto 3 cm from its original point when the sphere is dropped.

Answer 2

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Diameter of sphere = 18 cm

$\:\:$

• Sphere is dropped in cylindrical vessel partly filled with water

$\:\:$

• Diameter of cylindrical vessel = 36 cm

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• If the sphere is completely submerged then the water level rises

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

• Diameter of sphere = 18 cm

$\:\:$

Radius of sphere = $\sf \dfrac { Diameter } { 2 }$

$\:\:$

➨ Radius = 9 cm

$\:\:$

$\underline{\bold{\texttt{Volume of sphere :}}}$

$\:\:$

➠ $\sf \dfrac { 4 } { 3 } \pi r^3$

$\:\:$

r = Radius of sphere

$\:\:$

➜ $\sf \dfrac { 4 } { 3 } \pi 9^3$

$\:\:$

➜ $\sf \dfrac { 4 } { \cancel 3 } \pi \times \cancel 9 \times 9 \times 9$

$\:\:$

➜ $\sf 4 \times \pi \times 3 \times 9 \times 9$

$\:\:$

➨ 972π cm³ ------ (1)

$\:\:$

Diameter of cylindrical vessel = 36 cm

$\:\:$

Radius of cylindrical vessel = $\sf \dfrac { Diameter } { 2 }$

$\:\:$

➨ Radius = 18 cm

$\:\:$

$\underline{\bold{\texttt{Volume of cylindrical vessel :}}}$

$\:\:$

➠ πR²h

$\:\:$

R = Radius of cylindrical vessel

h = Height of water raised when sphere is dropped

$\:\:$

➨ π18²h cm³ ------- (2)

$\:\:$

Now ,

$\:\:$

• Volume of water rise = Volume of sphere

$\:\:$

〚 As water will rise in the cylindrical vessel only hence the volume of water rise can be calculated by volume of cylindrical vessel 〛

$\:\:$

$\underline{\bold{\texttt{Thus , (1) = (2)}}}$

$\:\:$

➜ 972π = π18²h

$\:\:$

➜ 972 = 18²h

$\:\:$

➜ $\sf h = \dfrac { 972 } { 18 \times 18 }$

$\:\:$

➜ $\sf h = \dfrac { 54 } { 18 }$

$\:\:$

➨ h = 3 cm

$\:\:$

• Hence the water in cylindrical vessel will rise upto 3 cm from its original point when the sphere is dropped.