Trapezoid Prism Problems, 2

Category: Solid Geometry

"Published in Newark, California, USA"

A contractor agrees to build a dam, 180 ft. long and 20 ft. high, 12 ft. wide at the bottom and 8 ft. wide at the top, for $9.75 a cubic yard. Find his profit if his costs were $10,000.

Solution:

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

Photo by Math Principles in Everyday Life

The area of the base which is a trapezoid is

The volume of a dam which is a trapezoid prism is

The volume of a dam in cubic yards is

The labor cost of building a dam is

Therefore, the contractor's profit in building a dam is

Triangular Prism Problems, 3

Category: Solid Geometry

"Published in Newark, California, USA"

A trough is formed by nailing together, edge to edge, two boards 11 ft. in length, so that the right section is a right triangle. If 15 gals. of water are poured into the trough and if the trough is held level so that a right section of the water is an isosceles right triangle, how deep is the water? (231 cu. in. = 1 gal.)

Photo by Math Principles in Everyday Life

Solution:

Consider the cross section of a trough which is the base of a triangular prism

Photo by Math Principles in Everyday Life

The cross section area of water in a trough is

The length of a trough in inches is

The volume of water in a trough in cubic inches is

Therefore, the height or deep of water in a trough is

Trapezoid Prism Problems

Category: Solid Geometry

"Published in Vacaville, California, USA"

A trench is 180 ft. long and 12 ft. deep, 7 ft. wide at the top and 4 ft. at the bottom. How many cubic yards of earth have been removed?

Solution:

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

Photo by Math Principles in Everyday Life

The amount of earth removed is in the shape of a prism whose base is a trapezoid. The area of the base which is a trapezoid is

The amount of earth removed which is the volume of a trapezoid prism is

Therefore, the amount of earth removed in cubic yards is

Polygon Prism Problems, 3

Category: Solid Geometry

"Published in Vacaville, California, USA"

One part of a quartz crystal is a hexagonal prism with a right section of 1.29 sq. in., an edge of 2.31 in., and a base of 1.41 sq. in. Find the altitude of the prism.

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 quartz crystal is

Therefore, the altitude of a quartz crystal is