+0

# what is the volume of a sphere?

0
414
6

what is the volume of a sphere?

Guest Dec 8, 2014

#3
+85624
+10

Archimedes provided a rather ingenious proof of this by noting that the volume of a hemisphere is equal to the sum of the differences in the cross-sections of a cylinder and an associated cone both having the same radius as the hemisphere, i.e....... pi*r^2h - (1/3)pi*r^2h = (2/3)pi*r^2h. But, the cylinder and the cone also have a height equal to this radius, so we have (2/3)pi*r^2h = (2/3)pi*r^2*r = (2/3)pi*r^3

So....twice this equals the volume of a whole sphere = 4/3pi*r^3

CPhill  Dec 8, 2014
Sort:

#1
+270
+10

Volume of the sphere = 4/3ㅠr^3

Where, r = radius of the sphere

Derivation for Volume of the Sphere
The differential element shown in the figure is cylindrical with radius x and altitude dy. The volume of cylindrical element is...

The sum of the cylindrical elements from 0 to r is a hemisphere, twice the hemisphere will give the volume of the sphere. Thus,

From the equation of the circle x2 + y2 = r2; x2 = r2 - y2.

flflvm97  Dec 8, 2014
#2
+17721
+5

The formula for the volume of a sphere is:  V  =  (4/3)·π·r³

geno3141  Dec 8, 2014
#3
+85624
+10

Archimedes provided a rather ingenious proof of this by noting that the volume of a hemisphere is equal to the sum of the differences in the cross-sections of a cylinder and an associated cone both having the same radius as the hemisphere, i.e....... pi*r^2h - (1/3)pi*r^2h = (2/3)pi*r^2h. But, the cylinder and the cone also have a height equal to this radius, so we have (2/3)pi*r^2h = (2/3)pi*r^2*r = (2/3)pi*r^3

So....twice this equals the volume of a whole sphere = 4/3pi*r^3

CPhill  Dec 8, 2014
#4
+92193
+5

Welcome to the forum fiflvm97.  I hope that ou like it here.      I can see that you will be a great asset to us if you choose to stay around :)

---------------------------------------------------------------------

I have been looking at these answers.

Geno, yours is concise but exactly what the asker would have wanted.

I hope that some of our senior students really think about what you said - as I did.  It would be of great benefit to them.

Chris,  I had not thought before about the volume of a cone being one third of a hemisphere.  It's an obvious conclusion now that you point it out.

As for the rest of what archimedes said that will require a more concentrated effort from me.  Thank you for discussing it.

Melody  Dec 8, 2014
#5
+85624
+5

Melody......there used to be a very good illustration of this on the net, but I'm unable to find it, now. However, this one is pretty good......http://mathcentral.uregina.ca/QQ/database/QQ.09.01/rahul1.html

CPhill  Dec 9, 2014
#6
+92193
0

Thanks chris - that is really neat :)

Melody  Dec 9, 2014

### 14 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details