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?


Answers:  

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)
1.33333333
"pi
3.14159265
r
48.2322777
(4/3)pir3
470004.4



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