Sunday, July 14, 2019

Radius of a one-ton gold sphere

This post considers the radius of a one ton sphere of gold.

Question:   A previous problem found that a ton of gold has a volume of 47,004.4 cubic centimeters.   Go here to better understand this interesting calculation.

Volume of one ton of gold.
http://www.dailymathproblem.com/2019/05/volume-of-one-ton-of-gold.html

What is the radius of a sphere consisting one ton of gold?

The volume of a sphere is V=(4/3)*pi*r3

Plugging in the value of the item and solving for r we get

r=(47,0004.4 * (3/4)/pi)1/3

This reduces to 48.323 cm3

Plugging this value of r into the formula for the volume of the sphere does in fact give us the correct volume.

 "(4/3) 1.33333 "pi 3.14159 r 48.2323 (4/3)pir3 470004