1. No category

G.GMD.3 STUDENT NOTES WS #3
1
THE CYLINDER
A cylinder has a lot of the same characteristics as a prism but is not a prism because of its circular base. The
cylinder and the prism both have two identical parallel bases and interesting enough they both have
rectangular lateral faces. The last point might be hard to visualize if
you think of unwrapping a soup can label or pulling the label from a
water bottle - the two dimensional form is a rectangle.
CYLINDER VOLUME – THE STACKING PRINCIPLE
The same stacking technique works great for cylinders as
well. All cross section parallel to the base are all congruent
circles and so using the same technique we are able to
determine the formula to be:
AREACYLINDER = Bh = πr2h
Cavalieri’s principle works with cylinders as well. The cross
section will be congruent circles and so the oblique cylinder
will have the same volume as the right cylinder.
CYLINDER VOLUME CALCULATION
The formula for the volume of a cylinder is also quite simple. The capital B
represents the AREA of the base but in this case the base will be a circle
and so we can substitute in πr2. The height, h, refers to the height of the
cylinder which the perpendicular distance between the two circular bases.
VCYLINDER = Bh
VCYLINDER = π r 2 h
Example #1
Example #2
Example #3
V = Bh
V = (Area of Circle)(height)
V = (πr2) (h)
V = π(4)2 (5)
V = 80π cm3
V = Bh
V = (Area of Circle)(height)
V = (πr2) (h)
V = π(3)2 (4)
V = 36π cm3
V = Bh + Bh - Bh
V = π(7)2 (11) + π(5)2 (5) - π(1)2
(16)
V = 648π cm3
G.GMD.3 WORKSHEET #3
NAME: ____________________________ Period ________
1. Determine the volume of the cylinder.
a)
b)
c)
Volume = ________________ (E)
Volume = ________________ (E)
Volume = _______________ (E)
d)
e)
f)
Volume = ________________ (E)
Volume = _______________ (E)
Volume = _______________ (E)
2. Determine the volume of the cylinder.
a)
b)
c)
Inner Radius = 2 cm
Inner Diameter = 2 cm
Volume = ________________ (E)
Volume = ________________ (E)
Volume = _______________ (E)
1
G.GMD.3 WORKSHEET #3
2
3. Determine the volume of the solid.
a)
b)
c)
Volume = ________________ (E)
Volume = ________________ (E)
Volume = _______________ (E)
d)
e)
f)
Volume = ________________ (E)
Volume = _______________ (E)
Volume = _______________ (E)
g) Diameter of hole = 2 cm
h) Square hole with sides of 3 cm
i) Two ≅ cylindircal holes,
diameter of holes is 6 cm.
Volume = ________________ (E)
Volume = _______________ (E)
Volume = _______________ (E)
J
*otr, fu*
G.GMD.3 WORKSHEET #3
PERtoD
1. Determine the volume of the cylinder.
a)
b)
I,.S $Yt
V
Vl an-L
-- tf ful,-
'=
=n k)'3)
Volume
=
I
lr
r
c,,*3
(E)
d)
Volume =
(E)
Volume
r (n'k)
= ZZfT
C,.u? (E)
e)
* 6,xcm
*.{
23fm
arrtrrrrrr.tr"trtrtrarrrtrrr,
V=6v-ln
=
Volume =
(E)
Volume
=
t Ca'(P)
?Sof crt (E)
Volume =
(E)
2. Determine the volume of the cylinder.
b)
c)
{.-gs*.*-*
-.-1
12
\1=
VarS-Vs'*il
Vc fir(il>(v) -
tbr*(
Volume
= {'lb \.
-
lnnerDiameter=2cm
r 0()'(,r)
V
Gl
Volume =
- lr
tf-k) - 'ir (Wr)
= Fon 577
[qL if
Cfi^>
VstL -Vs,*ru
5cm
lnnerRadius=2cm
cm
V'
ffi
(E)
Volume =
Z St.f
Celtrl
2
G.GMD.3 WORKSHEET #3
3. Determine the volume of the solid.
c)
a)
V:i ri (ztYE)
6am
(E)
V=- Bl,./
,r-
= [A(:i,-+2(
\z
l-l
=
f4r ?
Volume
=
+
Volume =
[{
tc
cwl
(E)
4\(,"t
cyu3 G')
Volume =
(E)
h) Square hole with sides of 3 cm
g) Diameter of hole = 2 cm
(E)
'=='firn)b)+n4'- ry)0t
= 6r,l + qo"fn_q.fr) (,r)
= (2u,1. + sar) 0r))
q)o-
lttfil WL
Volume =
ffir,y
:,1;Bk
Volume
=
40o*
,Yo7r
i)Two = cylindircal holes,
diameter of holes is 5 cm.
13
= (tb)'-il@)
Volume =
(E)
tr--t--'-'-'-'-*
Volume =
=
i
?:>
9{m
*
c\ey
(rn
bbrt-ilC
e
3z*-rf -_81 cn?rt1
Volume =
(E)