surface area of the sphere

016 Radius of the sphere circumscribing a regular triangular pyramid

Example 016
Find the area of the surface and the volume of the sphere circumscribed about a regular tetrahedron of edge 25 cm. See Figure 015.
 

Sphere circumscribed about a regular tetrahedron

 

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.
 

007 - 008 Volume and surface area of earth and balloon

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.
 

Derivation of Formula for Total Surface Area of the Sphere by Integration

The total surface area of the sphere is four times the area of great circle. To know more about great circle, see properties of a sphere. Given the radius r of the sphere, the total surface area is
 

 
 
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