The outer diameter of a spherical shell is 12 cm and its inner diameter is 8 cm.

Question:

The outer diameter of a spherical shell is 12 cm and its inner diameter is 8 cm. Find the volume of metal contained in the shell. Also, find its outer surface area.

Solution:

Outer radius of the spherical shell = 6 cm
Inner radius of the spherical shell = 4 cm

Volume of metal contained in the shell $=\frac{4}{3} \times \frac{22}{7}\left(6^{3}-4^{3}\right)$

$=\frac{88}{21} \times(216-64)$

$=\frac{88}{21} \times 152$

$=636.95 \mathrm{~cm}^{3}$

$\therefore$ Outer surface area $=4 \times \frac{22}{7} \times 6 \times 6$

$=452.57 \mathrm{~cm}^{2}$

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