More Cylinder Problems, 3

Category: Solid Geometry

"Published in Newark, California, USA"

An ice-storage plant removed from the center of a pond a mass of ice covering an area of 2 acres. If the ice had a uniform thickness of 2 ft., find the weight in tons of the ice removed. (Ice weighs 56 lbs. per cu. ft.; 1 ton = 2,240 lbs.; 1 acre = 43,560 sq. ft.)

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 the top of ice covering from the center of a pond is

The volume of an ice covering which is a cylinder is

The weight of an ice covering is

Therefore, the weight of an ice covering in metric tons is

More Cylinder Problems, 2

Category: Solid Geometry

"Published in Newark, California, USA"

During a rain, ¼ in. of water fell. Find how many gallons of water fell on a level 10-acre park. (Take 1 cu. ft. = 7.48 gals. and 1 acre = 43,560 sq. ft.)

Photo by Math Principles in Everyday Life

Solution:

Consider the given figure above

Photo by Math Principles in Everyday Life

Let's assume that the thickness of the rainwater within the level 10-acre park is ¼ in. Since the thickness of the rainwater is uniform, then the given figure is considered as a cylinder. 

In this case, the area of the base which is the level 10-acre park in square feet is

The volume of the rainwater which is a cylinder is

Therefore, the volume of the rainwater in gallons is

 

More Cylinder Problems

Category: Solid Geometry

"Published in Newark, California, USA"

A vertical stone column 12.5 ft. high has an elliptical base with the longer axis twice the shorter. If the weight of the column is 12,400 lbs. and if the stone weighs 160 lbs. per cu. ft., find the area of the largest and smallest axial section of the column.

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 ellipse which is the base of the column is

but

Hence, the above equation becomes

The volume of the column which is a cylinder is

The length of b which is the semi-minor axis of the ellipse is 

The length of a which is the semi-major axis of the ellipse is

Therefore, the area of the largest axial section of the column which is a rectangle is

Photo by Math Principles in Everyday Life

and the area of the smallest axial section of the column which is a rectangle is

Photo by Math Principles in Everyday Life