Q2 of 48 Page 270

A metallic sphere of radius 5.6 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Given.


Radius of sphere is 5.6 cm


Radius of cylinder is 6 cm


Formula used/Theory.


Volume of cylinder = πr2h


Volume of sphere = πr3


Volume of sphere = πr3


= × π × (5.6 cm)3


Volume of cylinder = πr2h


= π × (6 cm)2 × h


When a metallic sphere is recast in shape of cylinder


Volume of both sphere and cylinder will be equal


∴ comparing both we get height of cylinder


π × (6 cm)2 × h = × π × (5.6 cm)3


h =


h = 6.5 cm


∴ Height of cylinder is 6.5 cm


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