More Cube Problems, 3

Category: Solid Geometry, Physics

"Published in Newark, California, USA"

What is the weight of a block of ice 24 in. by 24 in. by 24 in., if ice weighs 92 percent as much as water, and water weighs 62.5 lb. per cu. ft.?

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

The first that we need to do is to get the volume of an ice which is a cube as follows

Since the density of ice is expressed in lb. per cu.ft., then we need to convert the volume of an ice in cu. ft. as follows

If the specific gravity of ice is 0.92, then the density of ice is

Therefore, the weight of ice is

More Cube Problems, 2

Category: Solid Geometry

"Published in Newark, California, USA"

Plato (429 - 348 B.C.) was one of the first to discover a solution to that famous problem of antiquity, the duplication of a cube, i.e., the finding of the edge of a cube whose volume is double that of a given cube. 
    
One legend asserts that the Athenians, who were suffering from a plague of typhoid fever, consulted the oracle at Delos as to how to stop the plague. Apollo replied that the Delians would have to double the size of his altar, which was in the form of a cube. A new altar was constructed having its edge twice as long as that of the old one. But the pestilence became worse than before, whereupon the Delians appealed to Plato. Given that the side of the altar was 8 ft., find, accurate to five figures, the edge of the required altar.

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

Consider the first cube or old altar:

Consider the second cube or new altar:

Therefore, the edge of the required or new altar is

More Cube Problems

Category: Solid Geometry

"Published in Vacaville, California, USA"

How much material was used in the manufacture of 24,000 celluloid dice, if each die has an edge of ¼ in.?

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

The volume of a cube is

Therefore, the amount of material used in making 24,000 celluloid dice is