May 2019
Problem of the Month

Bucket Problem
by Sam Lloyd

A bucket is 12 inches deep and holds exactly 25 gallons of water.

What is the diameter of the brim (to the nearest inch) if it is twice the diameter of the bottom?



You must show your work!

Solution to the Problem:

The diameter of the brim is 32.41 inches.

First, you must know that 1 gallon is equivalent to 231 cubic inches.   Therefore, 25 gallons (the volume of the bucket) is equivalent to 5,775 cubic inches.

The bucket is in the shape of a frustum of a cone (or a truncated cone), which is simply a cone with the top cut off parallel to the base.   See the diagram below.



To determine the volume of the bucket, find the volume of the large cone and subtract the volume of the smaller cone.



You could also solve the problem by using the formula for the volume of a frustum of a cone:

Correctly solved by:

1. James Alarie	Flint, Michigan
2. Kelly Stubblefield	Mobile, Alabama
3. Ivy Joseph	Pune, Maharashtra, India
4. Sapna Dominic	Mumbai, Maharashtra, India
5. Brijesh Dave	Mumbai City, Maharashtra, India
6. Adam Bates	Mountain View High School, Mountain View, Wyoming
7. Dennis Owens	Mountain View High School, Mountain View, Wyoming
8. Tyler Stoddard	Mountain View High School, Mountain View, Wyoming
8. Daniel Harris	Mountain View High School, Mountain View, Wyoming

Send any comments or questions to: David Pleacher