Question: How big is a container that contains a block of gold weighing one ton? How tall is the container if the base of the container is a square one meter by one meter?
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.
Extra Credit: What is the size 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
S = (47,004.4)(1/3)