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A spherical iron shell with external diameter 21 cm weighs \(22775\frac5{21}\) grams. Find the thickness of the shell if the metal weighs 10 gms per cu cm. 

(a) 3 cm 

(b) 1 cm 

(c) 2 cm 

(d) 2.5 cm

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(c) 2 cm.

Let the internal radius of the shell be r cm.

∴ Internal volume of the shell = \(\frac43πr^3\) cu. cm

External radius of the shell = \(\frac{21}{2}\) cm.

External volume of the shell = \(\frac43\times\frac{22}{7}\times\frac{21}{2}\times\frac{21}{2}\times\frac{21}{2}\) cu. cm

= 4851 cu. cm. 

Weight of 1 cu. cm of metal = 10g.

∴ Volume of the metal in the shell = \(22775\frac5{21}\times \frac{1}{10}\) cu. cm

\(\frac{478280}{21}\times\frac{1}{10}\) cu. cm = \(\frac{47828}{21}\) cu. cm

∴ Internal vol. of the shell = \(4851-\frac{47828}{21}=\frac{54043}{21}\) cu. cm

⇒ \(\frac43πr^3=\frac{54043}{21}\) ⇒ r\(\frac{54043\times3\times7}{21\times4\times22}\) = 614.125

⇒ \(r = 8.5 \) cm

∴ Thickness of shell = 10.5 cm – 8.5 cm = 2 cm

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