Question

Eight metallic spheres, each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere

Answer 1

$\bold{Answer:}$

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.

Answer 2

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