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  • A cylindrical tennis ball container contains three balls stacked on one another, such that they touch thewall of the container. The top and bottom balls also touch the lid and the base of thecontainer respectively. If the volume of a tennis ball is 160 cm

A cylindrical tennis ball container contains three balls stacked on one another, such that they touch thewall of the container. The top and bottom balls also touch the lid and the base of thecontainer respectively. If the volume of a tennis ball is 160 cm3, then what is the volume of the container?

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The volume of a tennis ball $$ = 160 cm^3

We know that the volume of the sphere$$=frac43 pi r^3

                                               $$160 = fraaac43 imes frac227 imes r^3 $$\ $$ r^3 = frac160 imes 3 imes 7 4 imes 22$$\ $$r^3 = frac40011 $$\ $$ r = 3.36$$\ $$ d =6.72

The diameter of the tennis ball  $$ d =6.72

The height of the cylinder $$ h= 3 imes 6.72 = 20.16cm

The radius of cylinder = Radius of ball

The volume of the cylinder

                           $$ V =pi r^2 h $$\ $$ V = frac227 imes (3.16)^2 imes 20.16 $$\ $$ V = 715.30 cm^3

Therefore, the volume of the container $$ V = 715.30 cm^3

 

Posted by

Deependra Verma

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