MAC 2312 Lecture 2: 6.2 Applications of Integration : Volumes
20 Jun 2018
School
Department
Course
Professor
5116118
volumnes
Wednesday
#
* cylinder in general ✓=A. h
|/in A
÷
't fifth
Circular Cylinder :
volume
°
. Tv ~
h-
New kind of question
A ( ×)
-Curvy
cylinder
^
•
|(•f¥§
,
✓
=SbaAc×÷
= lim {Alxi )bx
DX -70 i=i
Example :
^
Show that the volume of a ball with
radius ✓ is ✓ = ±ziTr3 ( Assuming area of a
o
,
adf.mnwits.radiasrisnen.tn
)
c.r.it#fkf
✓ =Sba Act )dx
aCross Section is a Circle
Y¥,. yis radius of circle at ×
AC×)-#y2= it (y2 -×2 )
✓ =[it (r2 -×2 )dx =2fro #(✓ 2.×2 )dx = 2 #[r2× -×÷ ][ o
\
Just Shows
=zit (✓
3
-¥)
it Can Just be moved
&multiplied by 2=±z is r
3
