*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.

S

^{3}=47,004.4 cubic centimeters
or

S = (47,004.4)

^{1/3}
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