# 012 Sphere circumscribed about a right circular cylinder

**Example 012**

Find the volume and total area of the sphere which circumscribes a cylinder of revolution whose altitude and diameter are each 6 inches.

**Solution 012**

Diameter of the sphere

$D^2 = 6^2 + 6^2$

$D^2 = 6^2 + 6^2$

$D = 6\sqrt{2} \, \text{ in}$

Volume of the sphere:

$V = \frac{1}{6}\pi D^3 = \frac{1}{6}\pi (6\sqrt{2})^3$

$V = 319.89 \, \text{ in}^3$ *answer*

Total surface area of the sphere:

$A = \pi D^2 = \pi (6\sqrt{2})^2$

$A = 226.19 \, \text{ in}^2$ *answer*

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