RIght Circular Cylinder Problems, 22

Category: Solid Geometry

"Published in Vacaville, California, USA"

A cylindrical tank, diameter 1 ft., length 6 ft., is placed so that its axis is horizontal. How many pounds of water will be used in filling it to a depth of 9 in., if water weighs 62.4 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

If a right circular cylinder whose axis is placed in a horizontal position, then its base is a circular segment. We need to get the area of its base first so that we can solve for the volume of water in a right circular cylinder. Let's analyze the cross section which is the base of a cylinder that is partially filled with water as follows

Photo by Math Principles in Everyday Life

By Pythagorean Theorem, the length of AD or DB is

Since ∆AOD or ∆BOD is a right triangle, then by using trigonometric function, the value of ∠AOD or ∠BOC is

The area of circular segment ABC is

The area of the base of a cylinder filled with water is

                          or

Hence, the volume of water in a right circular cylinder is

Therefore, the weight of water in a right circular cylinder is

     

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

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