derive formula of volume of a sphere using method of disks

Deriving the formula for the voluming of a sphere using the method of disks

Category:

Education

Tags:

• calculus
• volume
• sphere
• shells
• method
• of
• washers
• volumes
• revolution

[tarmozia]

great video i could not understand . how did you get y=^r2-x2.

thanks

[leettab]

@tarmozia the general formula for the area of a circle is r^2 = x^2 + y^2 where r is the radius and (x,y) is a point on the circle. We want to find an expression for the part of the circle above the x-axis. If we solve r^2 = x^2 + y^2

for y by subtracting x^2 from both sides and taking the square root we get y = squareroot(r^2 - x^2). I hope this

helps to answer your question.

[tarmozia]

@leettab

it did but shouldn't it be half b/s we are finding the upper circle only..

[leettab]

@tarmozia sorry. remember when we take the square root it will be +/- (plus or minus) the square root of

r^2 - x^2 so the part of the circle above the x axis has the formula PLUS squareroot(r^2 - x^2). The part below

the x-axis is MINUS squareroot(r^2 - x^2). Think back to when you take the square root of say 4. It is +/-2 because (-2)^2 = 4 and (2)^2 =4. Let me know if you have any further questions.

[iiCeMaN69z]

Thank you so much, you did something my prof. couldn't do!

[leettab]

@iiCeMaN69z your welcome. glad to be of help

[mufc4everch]

thanks

[tank44441]

im confused........ -Acid

[trevormovestuff]

As far as I can tell this is the only calc based proof of volume of a sphere on youtube. thank you!

[tarmozia]

@leettab THANK YOU again. it is much more understandable..