Q. 65.0( 1 Vote )

Answer :

Given: diameter of hemisphere = 30 cm

∴ Radius of hemisphere = r_{h} = 30/2 = 15cm

Diameter of cylindrical shaped bottles = 5 cm

∴ radius of cylindrical shaped bottles = 5/2 = r_{c} = 2.5 cm

Height of cylindrical shaped bottle = h = 6 cm

Formula: volume of hemisphere = (volume of sphere/2) = (2/3)πr_{h}^{3}

Volume of cylinder = πr_{c}^{2}h

Let ‘n’ bottles are required

As we are filling the cylindrical bottles with liquid in hemispherical bowl hence we can say that

volume of liquid in cylindrical bottles = volume of liquid in hemisphere

∴ n × π × r_{c}^{2} × h = (2/3) × π × r_{h}^{3}

n × 2.5^{2} × 6 × 3 = 2 × 15^{3}

n × 6.25 × 9 = 3375

n = 3375/56.25

n = 60

Therefore 60 cylindrical shaped bottles are required to fill the liquid from hemispherical bowl.

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