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A spherical iron shell with 8 cm external diameter weighs $186047$ g. Find the thickness of the shell if the density of metal is 12 g/cm3.

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6cm

2cm

1cm

5cm

answer is C.

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Detailed Solution

It is given a spherical iron shell.
External diameter is 8cm.
Weight=

186047

g.
Density of metal=12 g/cm3.
Let the inner radius is r cm.
Outer radius is

⇒ 82

⇒

4 cm
The volume of the metal of the sphere is

43 × π × [(r 2) 3 − (r 1) 3]

, where

r 1

is the inner radius and

r 2

is the outer radius of the metallic sphere.
Volume of the metal in spherical iron shell

⇒ 43 × 227 × [(4) 3 − (r) 3]

⇒ 8821 × [(4) 3 − (r) 3]

Mass = Density

×

Volume

186047 = 12 × 8821 × [(4) 3 − (r) 3]

130247 = 3527 × (64 − r 3)

64 − r 3 = 37

3 = 27

r = 3

Now, Thickness of metal = Outer radius - inner radius

⇒

(4 - 3)

⇒

1 cm
Therefore, the correct option is 3.

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