Question

A hemispherical bowl of internal radius 9 cm is filled with a liquid. This liquid is required to be filled in small cylindrical bottles of diameter 3 cm and height 4 cm. Find, how many bottles will be required to fill the whole liquid of the bowl ? (Use pi = 22/7)

Answer 1

No. of bottles
=Volume of hemisphere/volume of cylinder
=2/3πR^3/πr^2h
=2/3×9×9×9/1.5×1.5×4
=2×3×9×9/1.5×1.5×4
=486/9
=54

Answer 2

$\huge\mathfrak{Solution:}$

Radius of the hemispherical bowl, r = 9 cm

Therefore, volume of the bowl, V1 = 1/2 × 4/3 × pi × (9)^3 cm^3

Given, diameter of the cylindrical bottle, 2r1 = 3 cm and height h = 4 cm

Let n number of bottles be required to get filled by the liquid of the bowl

Therefore, volume of n bottles = n × pi × r1^2 × h

= n × pi × (3/2)^2 × 4 cm^3

Clearly, 2/3 × pi × (9)^3 = n × pi × (3/2)^2 × 4

or n = 2/3 × (9 × 9 × 9 × 2 × 2 / 3 × 3 × 4) = 54

Therefore, numbers of bottles = 54.

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