KnowledgeBoat Logo
|

Mathematics

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

Mensuration

41 Likes

Answer

Radius of metallic sphere (r) = 2 cm.

Volume of sphere = 43\dfrac{4}{3}πr3

∴ Volume of eight spheres (V) = 8 x 43\dfrac{4}{3}πr3

= 323\dfrac{32}{3}π(2)3

= 2563\dfrac{256}{3}π cm3.

Since 8 spheres are combined to form a new bigger sphere,

∴ Volume of new sphere = V.

Let the radius of the big sphere be R cm.

∴43πR3=2563π⇒R3=256π3×34π⇒R3=64⇒R3=(4)3⇒R=4 cm.\therefore \dfrac{4}{3}πR^3 = \dfrac{256}{3}π \\[1em] \Rightarrow R^3 = \dfrac{256π}{3} \times \dfrac{3}{4π} \\[1em] \Rightarrow R^3 = 64 \\[1em] \Rightarrow R^3 = (4)^3 \\[1em] \Rightarrow R = 4 \text{ cm}.

Hence, the radius of the new sphere = 4 cm.

Answered By

15 Likes

Related Questions