RIght Circular Cylinder Problems, 11

Category: Solid Geometry, Physics

"Published in Newark, California, USA"

When a body is immersed in water in a right circular cylinder 60 cm. in diameter, the level of the water rises 40 cm. What is the volume of the body?

Solution:

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

Photo by Math Principles in Everyday Life

If you have an object with irregular shape, let's say a stone, for example, then it is difficult to get its volume. In this case, the only way to get the volume of an object is by immersion method. You will need a right circular cylinder with water and measure its height. Next, immerse an object in water in a right circular cylinder and measure its height. The difference of their height will be used to calculate the change of the volume of water which is equal to the volume of an object.

Since the change of the level of water in a right circular cylinder is given in the problem, therefore, the volume of an object is

   

Right Circular Cylinder Problems, 10

Category: Solid Geometry

"Published in Vacaville, California, USA"

A cylindrical standpipe is to contain 343,000 gal. of water. If its height is to be twice its diameter, what must be its dimensions?

Solution:

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

Photo by Math Principles in Everyday Life

Since the given volume of water is in gallons, then we have to convert it first into cubic feet as follows

   

Hence, the diameter of a cylindrical standpipe is

and its height is

Therefore, the dimensions of a cylindrical standpipe are d = 30.791030 ft. and h = 61.58206 ft.