ICSE Board Question Based on Mensuration Chapter of M.L Aggarwal for class10
In this question given that eight metallic spheres, each of radius 2 cm, are melted and cast into a single sphere. Calculate the radius of the new (single) sphere.
This is the Question Number 07, Exercise 17.5 of M.L Aggarwal.
Deepak BoraNewbie
Eight metallic spheres, each of radius 2 cm, are melted and cast into a single sphere. Calculate the radius of the new (single) sphere.
Share
Given radius of each sphere, r = 2 cm
Volume of a sphere = (4/3)r3
= (4/3)×23
= (4/3)×8
= (32/3) cm3
Volume of 8 spheres = 8×(32/3)
= (256/3) cm3
Let R be radius of new sphere.
Volume of the new sphere = (4/3)R3
Since 8 spheres are melted and casted into a single sphere, volume remains same.
(4/3)R3 = (256/3)
4R3 = 256
R3 = 256/4 = 64
Taking cube root
R = 4 cm
Hence the radius of the new sphere is 4 cm.