Question

the internal and external radii of a hollow spherical shell are 3 cm and 5cm respectively. if it is melted and recast into a solid cylinder of diameter 14 cm . find the heigt of the cylinder

Answer 1

Answer:

Step-by-step explanation:

Volume of the material of hollow sphere = (4/3)π ×(R³ - r³)

                                                                = (4/3)π×(5³ -3³)                                                                                                                     = 392π/3 cm³

now it is melted to form cylinder ,

so volume of cylinder = volume of the material of sphere

⇒π r² ×h =392π/3 cm³

⇒r² = (392×3)/( 32×3)

     = 12.25

⇒r =√12.25 = 3.5 cm

so diameter of cylinder = 3.5×2 = 7 cm

Answer 2

when we melt and into a another solid the volume remain same
vol. of spherical shell = vol. of cylinder
4/3 π (R^3 - r^3) = π r^2 h
4/3 (125-27) = 7*7 ×h
8/3 =h
height of cylinder is 8/3 cm