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A hemispherical bowl of internal radius 12 cm is full of a liquid. This liquid is to be filled into conical bottles each of radius 6 cm and height 8 cm. How many such bottles are required to empty the bowl?

A hemispherical bowl of internal radius 12 cm is full of a liquid. This liquid is to be filled into conical bottles each of radius 6 cm and height 8 cm. How many such bottles are required to empty the bowl? Correct Answer 12

Given:

Internal Radius of Hemispherical Bowl = 12 cm

Height of Conical Bottle = 8 cm

Radius of Conical Bottle = 6 cm

Concept used:

Number of Conical Bottles = (Volume of Hemispherical Bowl)/(Volume of one Conical Bottle)

Formula used:

Volume of Hemispherical Bowl = (2/3)πR3

Volume of Cone = (1/3)πr2h

Where:

R = Radius of Hemispherical Bowl

r = Radius of Cone, h = Height of Cone

Calculation:

Volume of Hemispherical Bowl = (2/3) × (π × 123)

⇒ (2/3) × 1728π = 1152π

Volume of Cone = (1/3) × (π × 62 × 8)

⇒ (1/3) × 288π = 96π

Number of Conical Bottle = (1152π)/96π = 12

∴ The number of Bottles required is 12

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