Example 007 A spherical balloon is inflated so that so that its diameter is 12 m. Find the surface area of the balloon’s covering and the volume of the gas.

Solution 007

$A = 452.39 \, \text{ m}^2$ answer

Volume of gas $V = \frac{1}{6}\pi D^3 = \frac{1}{6}\pi (12^3)$

$V = 904.78 \, \text{ m}^3$ answer

Example 008 Find the volume and total surface area of the earth. (Consider the earth a perfect sphere of diameter 7960 miles.)

Solution 008

$A = 199.06 \times 10^6 \, \text{ miles}^2$ answer

Volume of gas $V = \frac{1}{6}\pi D^3 = \frac{1}{6}\pi (7960^3)$

$V = 2.64 \times 10^{11} \, \text{ miles}^3$ answer

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