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From each end of a solid metal cylinder, metal was scooped out in hemispherical from of same diameter. The height of the cylinder is 10 cm and its base is of radius 4.2 cm. - Mathematics

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From each end of a solid metal cylinder, metal was scooped out in hemispherical from of same diameter. The height of the cylinder is 10 cm and its base is of radius 4.2 cm.
The rest of the cylinder is melted and converted into a cylindrical wire of 1.4 cm thickness. Find the length of the wire [Use  π=22/7]

 

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Solution

Height of the cylinder (h) = 10 cm
Radius of the base of the cylinder = 4.2 cm

Volume of the cylinder =`pir^2h`

`=22/7xx(4.2)^2xx10`

`=554.4 cm^3`

Volume of hemisphere=`2/3pir^2`

`=2/3xx22/7xx(4.2)^2`

`=155.232 cm^3`

Volume of the remaining cylinder after scooping out the hemisphere from each end
Volume of original cylinder - 2 x Volume of hemisphere

=554.4 - 2 x 155.232

=243.936 cm3

The remaining cylinder is melted and converted to
a new cylindrical wire of 1.4 cm thickness.
So they have same volume and radius of new cylindrical wire is 0.7 cm.
Volume of the remaining cylinder = Volume of the new cylindrical wire

`243.936=pir^2h`

`243.936=22/7(0.7)^2h`

h=158.4 cm

∴The length of the new cylindrical wire of 1.4 cm thickness is 158.4 cm.

Concept: Conversion of Solid from One Shape to Another
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