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

Answer:

54

Step-by-step explanation:

Volume of the liquid = Volume of  hemispherical bowl =

                                  =2/3*22/7*9³ =1527.42cm³

Volume of one cylindrical shaped ball=

                                   = 22/7*1.5*1.5*4   =28.28cm³

number of bottles needed = Volume of  hemispherical bowl / Volume of one                                                                                                  cylindrical shaped ball

                                          =1527.42 / 28.28

                                           = 54.01

 Therefore , number of bottles needed  = approx 54 bottles

Answer 2

$\huge\mathfrak{Solution:}$

Radius of the hemispherical bowl, r = 9 cm

Therefore, volume of the bowl, V1 = 1/2 × 4/3 × pi × r^3

= 2/3 × 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, volume of the liquid in the bowl = volume of n bottles

Therefore, 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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