Question

A hollow spherical shell is made of a metal of density 4.5g per cm cube .If its internal and external radii are 8 cm and 9 cm respectively find the weight of the shell

Answer 1

let r and R be the internal and external radii of hollow spherical shell.

since , internal radius of the shell = 8cm

external radius of the shell = 9 cm

Find the volume of the shell:
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volume of the shell = 4/3 πR^3 - 4/3πr^3

= 4/ 3 π( R^3 - r^3 )

= 4 /3 π [ (9)^3 - (8)^3 ]

= 4 / 3 π ( 729 - 512 )

= (4 /3) π × 217 = (4/3 )× 217 × (22/ 7)

= 2728 / 3 cm^3

Given , weight of 1cm^3 = 4.5g ,then

Find the weight of the shell:
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weight of the shell

= (2728/ 3) × 4.5 = 4092 g

therefore, weight of the spherical shell

= 4092 g

Answer : weight = 4092 g
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