Q. 135.0( 3 Votes )

Answer :

Given: Radius of hemisphere = r_{h} = 9 cm

Diameter of cylindrical shaped bottles = 3 cm

∴ radius of cylindrical shaped bottles = r_{c} = 3/2 = 1.5 cm

Height of cylindrical shaped bottle = h = 4 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 × (3/2)^{2} × 4 × 3 = 2 × 9^{3}

n = 3^{3} × 2

n = 27 × 2

n = 54

Therefore 54 cylindrical shaped bottles are required to fill the liquid from hemispherical bowl.

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