Eight metallic spheres, each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere
Eight metallic spheres, each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere
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Radius of 1 metallic sphere = 2cm
volume= 4/3 π r ^3
= 4/3 x 22/7 x 2 x 2 x 2 = 88 x 8/21
volume of 8 spheres = 88 x 8 x 8/21
let the radius of new sphere= y
Volume = 4/3 π y^3
= 4/3 x 22/7 y^3
= 88/21 y^3
88/21 y^3 = 88 x 8 x 8/21
y^3 = 88 x 8 x 8/21 x 21/88
y^3 = 64
y = cube root(64) = 4
y = 4cm.
Of radius 2mm
volume if one metallic sphere = 4/3 πr³
= 4/3 × 3.14 × 2³
= 4/3 × 3.14 × 8 = 33.49 mm³
Volume of eight metallic sphere having radius 2mm = 33.49 × 8 = 267.94 mm³
Since eight spheres are melted and casted into single sphere.
That means single sphere has same volume as that of volume of eight spheres
•°• Volume of new sphere = 267.94mm³
4/3 πr³ = 267.94
4/3 × 3.14 × r³ = 267.94
r³ = 267.94/4.18
r³ = 64.100 approximate 64
r³ = 64
r = ³√64
r = 4mm
Therefore, radius of new sphere is 4mm