A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 4 cm. How many bottles will be needed to empty the bowl?

Given

Radius of hemispherical bowl = 9 cm

Hence,

volume of the bowl = (2/3)πr3

= (2/3) x (22/7) x 9 x 9 x 9

= 1527.42 cm3

Since height of the bottle (h) = 4 cm and diameter of the cylindrical bottles = 3 cm

So, radius = 1.5 cm

Hence, the volume of the cylindrical bottle = πr2h

= 22/7 x 1.5 x 1.5 x 4

Let the number of cylindrical bottle be (n)

⇒ n = Volume of hemispherical bowl/Volume of one cylindrical bottle

n = (2/3)πr3/πr2h = {(2/3) x (22/7) x 9 x 9 x 9}/{(22/7) x 1.5 x 1.5 x 4}

n = (2 x 9 x 9 x 9)/(3 x 1.5 x 1.5 x 4)

We get,

n = 54

Therefore, the number of bottle is 54

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