## Thursday, May 2, 2019

### Volume of one ton of gold

Some questions on the dimensions of one-ton of gold set as a rectangular box and as a cube.

Question:  How tall is a box with a ton of gold if the base of the box is a square meter?

What is the length of the side of a cube of gold weighing one ton?

Answer:  There are 19.30 grams of gold per cubic centimeter which means 1/19.30 cubic centimeters will hold one gram of gold.  There are 907,185 grams in one ton.

Looking at the dimensions we see that cc/ton = (cc/gram) x (gram/ton).  The number of cubic centimeters needed to hold one ton of gold is

(1/19.30) x 907,185 = 47,004.4 cubic centimeters

The base of the container is 10,000 square centimeters.  (There are one hundred centimeters in a meter and 100 centimeters x 100 centimeters is equal to 10,000 square centimeters.)

The volume of the box needed to hold 47,004.4 cubic centimeters of gold is

Volume=L x W x H = 100 x 100 x H = 10,000 x H

Solve for H by dividing each side by 10,000.

H=47,004.4/10,000=4.7004 centimeters

Extra Credit:  What is the length, width and height of of a square cube of gold weighing one ton?

Answer:  Each side of the cube (denoted s) is identical.

S3=47,004.4 cubic centimeters

or

S = (47,004.4)1/3