Voollumes (1 Viewer)

[Rax]

Hello Everybody

Started Volumes last week.

Just had one question

A hole of radius a/2 is bored through the centre of a sphere of radius a. Fine the volume of the remaning solid.

I am meant to be doing this by using slices not cylindrical shells.

Any ideas? I just can't get it off the ground

Thanks all

GG

 

[_ShiFTy_]

I think you use slicing

Draw x² + y² = a² and dot x = -a/2 and +a/2
Your strip should be between any edge of the circle and x = -a/2
Spin this around the y axis and you should get:

Δv = π(x² - a²/4)Δy

*x² + y² = a²

2π ₀∫^a (3a²/4 - y²) dy

I got 5π/6 . a³ as the answer... :S

 

[Rax]

Yeah funny enough I did somethin similiar to that, and the answer is

(sqrt3)π/2 . a3

so its dodging me

 

[_ShiFTy_]

Draw a picture. Check your limits of integration - where does x=a/2 meet the circle?

Whoops...totally forgot about the change of limits

 

[Rax]

Na, don't worry. My Teacher showed me how to do it properly.

I was doing it so wrong lol.

My bad.

GG