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opp ruimtefiguren
opp ruimtefiguren
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opp ruimtefiguren
Slide 1 - Slide
Deze kubus wordt rood geschilderd.
Wat moeten we berekenen?
A
Oppervlakte
B
Omtrek
C
Inhoud
Slide 2 - Quiz
Slide 3 - Video
7.3: Opp. ruimtefiguren
Stappenplan:
Schrijf de afzonderlijke grensvlakken op.
Bekijk welke dezelfde vorm hebben.
Bereken de oppervlakte van alle grensvlakken.
Denk aan de formules en maak eventueel schetsen.
Tel de oppervlaktes bij elkaar op.
Schrijf je conclusie op.
Slide 4 - Slide
7.3: Opp. cilinder
o
p
p
.
b
o
v
e
n
=
π
⋅
s
t
r
a
a
l
2
=
π
⋅
1
,
2
5
2
=
4
,
9
0
8
.
.
.
o
p
p
.
o
n
d
e
r
=
4
,
9
0
8
.
.
.
o
p
p
.
z
i
j
=
l
⋅
b
=
π
⋅
2
,
5
⋅
3
=
2
3
,
5
6
1
.
.
.
o
p
p
.
c
i
l
i
n
d
e
r
=
4
,
9
0
8
.
.
.
+
4
,
9
0
8
.
.
.
+
2
3
,
5
6
1
.
.
.
=
3
3
,
4
3
7
9
.
.
.
straal = 2,5 : 2 = 1,25 cm
Dus de opp. is ca. 33,4 cm
2
Slide 5 - Slide
7.3: Opp. cilinder
o
p
p
.
b
o
v
e
n
=
π
⋅
s
t
r
a
a
l
2
=
π
⋅
1
,
2
5
2
=
4
,
9
0
8
.
.
.
o
p
p
.
o
n
d
e
r
=
4
,
9
0
8
.
.
.
o
p
p
.
z
i
j
=
l
⋅
b
=
π
⋅
2
,
5
⋅
3
=
2
3
,
5
6
1
.
.
.
o
p
p
.
c
i
l
i
n
d
e
r
=
4
,
9
0
8
.
.
.
+
4
,
9
0
8
.
.
.
+
2
3
,
5
6
1
.
.
.
=
3
3
,
4
3
7
9
.
.
.
straal = 2,5 : 2 = 1,25 cm
Dus de opp. is ca. 33,4 cm
2
Slide 6 - Slide
7.3: Opp. cilinder
o
p
p
.
b
o
v
e
n
=
π
⋅
s
t
r
a
a
l
2
=
π
⋅
1
,
2
5
2
=
4
,
9
0
8
.
.
.
o
p
p
.
o
n
d
e
r
=
4
,
9
0
8
.
.
.
o
p
p
.
z
i
j
=
l
⋅
b
=
π
⋅
2
,
5
⋅
3
=
2
3
,
5
6
1
.
.
.
o
p
p
.
c
i
l
i
n
d
e
r
=
4
,
9
0
8
.
.
.
+
4
,
9
0
8
.
.
.
+
2
3
,
5
6
1
.
.
.
=
3
3
,
4
3
7
9
.
.
.
straal = 2,5 : 2 = 1,25 cm
Dus de opp. is ca. 33,4 cm
2
Slide 7 - Slide
7.3: Opp. cilinder
o
p
p
.
b
o
v
e
n
=
π
⋅
s
t
r
a
a
l
2
=
π
⋅
1
,
2
5
2
=
4
,
9
0
8
.
.
.
o
p
p
.
o
n
d
e
r
=
4
,
9
0
8
.
.
.
o
p
p
.
z
i
j
=
l
⋅
b
=
π
⋅
2
,
5
⋅
3
=
2
3
,
5
6
1
.
.
.
o
p
p
.
c
i
l
i
n
d
e
r
=
4
,
9
0
8
.
.
.
+
4
,
9
0
8
.
.
.
+
2
3
,
5
6
1
.
.
.
=
3
3
,
4
3
7
9
.
.
.
straal = 2,5 : 2 = 1,25 cm
Dus de opp. is ca. 33,4 cm
2
Slide 8 - Slide
7.3: Opp. cilinder
o
p
p
.
b
o
v
e
n
=
π
⋅
s
t
r
a
a
l
2
=
π
⋅
1
,
2
5
2
=
4
,
9
0
8
.
.
.
o
p
p
.
o
n
d
e
r
=
4
,
9
0
8
.
.
.
o
p
p
.
z
i
j
=
l
⋅
b
=
π
⋅
2
,
5
⋅
3
=
2
3
,
5
6
1
.
.
.
o
p
p
.
c
i
l
i
n
d
e
r
=
4
,
9
0
8
.
.
.
+
4
,
9
0
8
.
.
.
+
2
3
,
5
6
1
.
.
.
=
3
3
,
4
3
7
9
.
.
.
straal = 2,5 : 2 = 1,25 cm
Dus de opp. is ca. 33,4 cm
2
Slide 9 - Slide
7.3: Opp. cilinder
o
p
p
.
b
o
v
e
n
=
π
⋅
s
t
r
a
a
l
2
=
π
⋅
1
,
2
5
2
=
4
,
9
0
8
.
.
.
o
p
p
.
o
n
d
e
r
=
4
,
9
0
8
.
.
.
o
p
p
.
z
i
j
=
l
⋅
b
=
π
⋅
2
,
5
⋅
3
=
2
3
,
5
6
1
.
.
.
o
p
p
.
c
i
l
i
n
d
e
r
=
4
,
9
0
8
.
.
.
+
4
,
9
0
8
.
.
.
+
2
3
,
5
6
1
.
.
.
=
3
3
,
4
3
7
9
.
.
.
straal = 2,5 : 2 = 1,25 cm
Dus de opp. is ca. 33,4 cm
2
Slide 10 - Slide
7.3: Opp. cilinder
o
p
p
.
b
o
v
e
n
=
π
⋅
s
t
r
a
a
l
2
=
π
⋅
1
,
2
5
2
=
4
,
9
0
8
.
.
.
o
p
p
.
o
n
d
e
r
=
4
,
9
0
8
.
.
.
o
p
p
.
z
i
j
=
l
⋅
b
=
π
⋅
2
,
5
⋅
3
=
2
3
,
5
6
1
.
.
.
o
p
p
.
c
i
l
i
n
d
e
r
=
4
,
9
0
8
.
.
.
+
4
,
9
0
8
.
.
.
+
2
3
,
5
6
1
.
.
.
=
3
3
,
4
3
7
9
.
.
.
straal = 2,5 : 2 = 1,25 cm
Dus de opp. is ca. 33,4 cm
2
Slide 11 - Slide
7.3: Opp. cilinder
o
p
p
.
b
o
v
e
n
=
π
⋅
s
t
r
a
a
l
2
=
π
⋅
1
,
2
5
2
=
4
,
9
0
8
.
.
.
o
p
p
.
o
n
d
e
r
=
4
,
9
0
8
.
.
.
o
p
p
.
z
i
j
=
l
⋅
b
=
π
⋅
2
,
5
⋅
3
=
2
3
,
5
6
1
.
.
.
o
p
p
.
c
i
l
i
n
d
e
r
=
4
,
9
0
8
.
.
.
+
4
,
9
0
8
.
.
.
+
2
3
,
5
6
1
.
.
.
=
3
3
,
4
3
7
9
.
.
.
straal = 2,5 : 2 = 1,25 cm
Dus de opp. is ca. 33,4 cm
2
Slide 12 - Slide
7.3: Opp. cilinder
o
p
p
.
b
o
v
e
n
=
π
⋅
s
t
r
a
a
l
2
=
π
⋅
1
,
2
5
2
=
4
,
9
0
8
.
.
.
o
p
p
.
o
n
d
e
r
=
4
,
9
0
8
.
.
.
o
p
p
.
z
i
j
=
l
⋅
b
=
π
⋅
2
,
5
⋅
3
=
2
3
,
5
6
1
.
.
.
o
p
p
.
c
i
l
i
n
d
e
r
=
4
,
9
0
8
.
.
.
+
4
,
9
0
8
.
.
.
+
2
3
,
5
6
1
.
.
.
=
3
3
,
4
3
7
9
.
.
.
straal = 2,5 : 2 = 1,25 cm
Dus de opp. is ca. 33,4 cm
2
Slide 13 - Slide
7.3: Opp. cilinder
o
p
p
.
b
o
v
e
n
=
π
⋅
s
t
r
a
a
l
2
=
π
⋅
1
,
2
5
2
=
4
,
9
0
8
.
.
.
o
p
p
.
o
n
d
e
r
=
4
,
9
0
8
.
.
.
o
p
p
.
z
i
j
=
l
⋅
b
=
π
⋅
2
,
5
⋅
3
=
2
3
,
5
6
1
.
.
.
o
p
p
.
c
i
l
i
n
d
e
r
=
4
,
9
0
8
.
.
.
+
4
,
9
0
8
.
.
.
+
2
3
,
5
6
1
.
.
.
=
3
3
,
4
3
7
9
.
.
.
straal = 2,5 : 2 = 1,25 cm
Dus de opp. is ca. 33,4 cm
2
Slide 14 - Slide
7.3: Opp. cilinder
o
p
p
.
b
o
v
e
n
=
π
⋅
s
t
r
a
a
l
2
=
π
⋅
1
,
2
5
2
=
4
,
9
0
8
.
.
.
o
p
p
.
o
n
d
e
r
=
4
,
9
0
8
.
.
.
o
p
p
.
z
i
j
=
l
⋅
b
=
π
⋅
2
,
5
⋅
3
=
2
3
,
5
6
1
.
.
.
o
p
p
.
c
i
l
i
n
d
e
r
=
4
,
9
0
8
.
.
.
+
4
,
9
0
8
.
.
.
+
2
3
,
5
6
1
.
.
.
=
3
3
,
4
3
7
9
.
.
.
straal = 2,5 : 2 = 1,25 cm
Dus de opp. is ca. 33,4 cm
2
Slide 15 - Slide
7.3: Opp. cilinder
o
p
p
.
b
o
v
e
n
=
π
⋅
s
t
r
a
a
l
2
=
π
⋅
1
,
2
5
2
=
4
,
9
0
8
.
.
.
o
p
p
.
o
n
d
e
r
=
4
,
9
0
8
.
.
.
o
p
p
.
z
i
j
=
l
⋅
b
=
π
⋅
2
,
5
⋅
3
=
2
3
,
5
6
1
.
.
.
o
p
p
.
c
i
l
i
n
d
e
r
=
4
,
9
0
8
.
.
.
+
4
,
9
0
8
.
.
.
+
2
3
,
5
6
1
.
.
.
=
3
3
,
4
3
7
9
.
.
.
straal = 2,5 : 2 = 1,25 cm
Dus de opp. is ca. 33,4 cm
2
Slide 16 - Slide
7.3: Opp. cilinder
o
p
p
.
b
o
v
e
n
=
π
⋅
s
t
r
a
a
l
2
=
π
⋅
1
,
2
5
2
=
4
,
9
0
8
.
.
.
o
p
p
.
o
n
d
e
r
=
4
,
9
0
8
.
.
.
o
p
p
.
z
i
j
=
l
⋅
b
=
π
⋅
2
,
5
⋅
3
=
2
3
,
5
6
1
.
.
.
o
p
p
.
c
i
l
i
n
d
e
r
=
4
,
9
0
8
.
.
.
+
4
,
9
0
8
.
.
.
+
2
3
,
5
6
1
.
.
.
=
3
3
,
4
3
7
9
.
.
.
straal = 2,5 : 2 = 1,25 cm
Dus de opp. is ca. 33,4 cm
2
Slide 17 - Slide
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