Q5 of 48 Page 267

A metallic sphere of radius 15 cm is melted and a wire of diameter 1 cm is drawn from it. Find the length of the wire.

Given.


Cylindrical wire of diameter 1 cm


Metallic spherical of radius 15 cm


Formula used/Theory.


Volume of cylinder = πr2h


Volume of sphere = πr3


Let the length of wire be x


Volume of cylinder = πr2h


= π × ( cm) 2 × x


= π cm2


Volume of sphere = πr3


= π (15 cm) 3


= 4500π cm3


**Note we will not put value of π as it will be divided in next step


As we melt the metallic sphere in cylindrical wire the volume of both will be equal


∴ equating both we will get the length of wire


Volume of wire = Volume of metallic sphere


π cm2 = 4500π cm3


x = 4500 × 4


x = 18000 cm = 180 m


∴ length of wire is 180 m


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