Volume 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


015 Two unequal balls inside the cylinder

Example 015
Two balls, one 15 cm in diameter and the other 10 cm in diameter, are placed in a cylindrical jar 20 cm in diameter, as shown in Figure 014. Find the volume of water necessary to cover them.



014 Water poured into a jar of marbles

Example 014
A boy who had discovered that 20 mm marbles fitted snugly into the bottom of a cylindrical jar, dropped in a fourth on top of the three and poured water enough into the jar to just cover them. How much water did he use?

013 Insciribed and circumscribed sphere about a cube - volume comparison

Example 013
Compare the volume of a sphere inscribed in a cube with volume of the sphere that circumscribes the cube.

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.

005 Weight of ivory billiard balls

Example 005
A cubic foot of ivory weighs 114 lb. Find the weight of 1000 ivory billiard balls 2½ inch in diameter.

003 Weight of an iron shell

Example 003
An iron ball 10 cm in diameter weighs 4 kg. Find the weight of an iron shell 5 cm thick whose external diameter is 50 cm.