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A hemispherical bowl of internal diameter $36 cm$ contains liquid. This liquid is filled into cylindrical shaped bottles of radius $3 cm$ and height $6 cm$ . How many bottles are required to empty the bowl?

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answer is D.

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Detailed Solution

Given that a hemispherical bowl of internal diameter

36 cm

and cylindrical shaped bottles of radius

3 cm

and height

6 cm

.
We have the following formulae,
Volume of a hemisphere =

23 π r 3

Volume of a cylinder =

π r 2 h

Volume of hemisphere =

n ×

volume of cylindrical bottle

23 × π (18) 3 = n π × (3) 2 × 6 ⇒ 23 × (18) 3 = n × (3) 2 × 6 ⇒ n = 23 × 18 × 18 × 18 9 × 6 n = 72

Thus, the number of bottles required is 72.
Therefore the correct option is 4.

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