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.

009 Price of Oranges

Example 009
A store sells the same quality of oranges graded as to size. A grade of orange 2½-inch in diameter sells \$3.00 per dozen. What should be the cost of grade 2-inch in diameter?

006 Weight of steel ball bearings

Example 006
A steel plant has to fill an order from an automobile manufacturer for 100 000 steel ball bearings 12 mm in diameter. What is the total weight of the metal required to fill this order, if steel weighs 75.5 kN/m3?

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.

002 Weight of snow ball

Problem 002
Find the weight of the snowball 1.2 m in diameter if the wet compact snow of which this ball is made weighs 480 kg/m3

001 Solid steel ball remolded into hollow steel ball

Problem 001
A 523.6 cm3 solid spherical steel ball was melted and remolded into a hollow steel ball so that the hollow diameter is equal to the diameter of the original steel ball. Find the thickness of the hollow steel ball.

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

Derivation of Formula for Volume of the Sphere by Integration

For detailed information about sphere, see the Solid Geometry entry, The Sphere.

The formula for the volume of the sphere is given by

23 - Sphere cut into a pyramid

Problem 23
A sphere is cut in the form of a right pyramid with a square base. How much of the material can be saved?


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