Math Principles

Sunday, February 15, 2015

Right Circular Cylinder Problems, 21

Category: Solid Geometry

"Published in Vacaville, California, USA"

The height of a hot-water boiler attached to a furnace is 5 ½ ft. The circumference of the boiler is 48 in. If the metal is ⅛ in. thick, how many gallons will the boiler contain when full? (One gallon = 231 cubic inches)

Solution:

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

Photo by Math Principles in Everyday Life

Since the radius of a boiler is not given in the problem but the circumference is given, then we can solve for the radius as follows

If the thickness of a boiler is given also in the problem, then we can solve for the inner radius as follows

as well as the inner height as follows

Hence, the volume of water in the boiler when full in cubic inches is

Therefore, the volume of water in the boiler when full in gallons is

Saturday, February 14, 2015

Rectangular Parallelepiped Problem, 16

Category: Solid Geometry

"Published in Newark, California, USA"

How many bricks each 8 in. by 2 ¾ in. by 2 in. will be required to build a wall 22 ft. by 3 ft. by 2 ft. (not allowing for mortar)?

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 block of brick is

The volume of a wall made from bricks is

Therefore, the number of bricks used to build a wall is

Friday, February 13, 2015

Trapezoid Prism Problems, 7

Category: Solid Geometry

"Published in Newark, California, USA"

A corncrib 20 ft. long has a cross section which is represented in the figure. The crib is entirely filled with corn on the ear. How many bushels of corn does it contain, if 2 bu. of corn on the ear are equal to 1 bu. of shelled corn? (Use the approximation, 1 bu = 1 ¼ cu. ft.)