chapter 12 test: instructions: leave all answers in terms of π and reduce all fractions
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Name: Period:. Chapter 12 Test: Instructions: Leave all answers in terms of π and reduce all fractions. Surface area and Volume Good luck. No work=No credit. Part 1: Matching. A.) Type of solid. B.) Congruent polygons & //. C.) Faces, not including bases - PowerPoint PPT PresentationTRANSCRIPT
Chapter 12 Test: Instructions:
Leave all answers in terms of π and reduce all fractions.
Surface area and Volume
Good luck.
No work=No credit.
Name:
Period:
Part 1: Matching1.)prism
2.)bases
3.)altitude
4.)lateral faces
5.)lateral edges
6.)right prism
7.)oblique prism
A.) Type of solid.
B.) Congruent polygons & //.
C.) Faces, not including bases
D.) Where adjacent lateral faces intersect in // segments.
E.) Lateral faces not rectangles
F.) Lateral faces are rectangles.
G.) Segment _I_ to and joining two base planes.
Volume=Bh =(2k2k)(2k) =8k3 units3
Total Area=LA+2B =ph+2B =8k(2k)+2(2k)(2k) =16k2+8k2
=24k2 units2
Sample problem for 1 and 2: Find the volume and total area of a cube
with edge 2k.
2k
2k
2k
2k
2k2k
2k
1.) Find the volume of this rectangular prism
10
4
3
Bases
2.) Find the Lateral area and Total area of this rectangular prism
10
4
3
Bases
Sample problem A right triangular prism has height 20 and base edges 5, 12, 13. Total area?
TA=LA+2B
=ph+2(1/2bh)
=30(20)+2(1/2)(5)(12)
=600+60
=660 units25cm
13cm
12cm
20cm
Sample problem A right triangular prism has height 10 and base
edges 3, 4, 5. TA?Total area=_______
3cm5cm
4cm
10cm
Sample problem for 4. Find the Lateral Area of a triangular prism
LA=ph
=(8+8+6)(12)
=22(12)
=264 units2
8 8
6
12
4. Find Lateral Area of the triangular prism
16
16
12
20
Sample problem.Find the missing variable for each prism.5.) B=9 in.2
V=81 in.3
h=
6.) V=121 B= h=11
7.) LA=180ml p= h=9ml
V=Bh 81=9h h=9 in.
9 9
V=Bh 121=B(11) B=11 in.
11 11
LA=ph
180= p(9)
9 9 p=20 ml
Find the missing variable for each prism.5.) B=9 V=63 h=
6.) V=225 B= h=11
7.) LA=729 p= h=9
Sample problem: Find the volume of a Cylinderh2+42=52
h2+16=25
-16 -16
√H2 = √9
H = 3
V=Bh
=πr2h
=π(2)2(3)
=12π ft.3
5 ft
4 ft
d=______r=______h=______
h=___ ft
8. Find the volume of a Cylinder
25 ft
24 ft
d=______r=______h=______
h=___ ft
Sample problem: If the ratio of radii of two similar cylinders is 1:2
a.) Ratio of corresponding Perimeters? 1:2
b.) Ratio of areas? 12:22 = 1:4
c.) Ratio of volumes? 13:23 = 1:8
If the volume of the smaller cylinder is 48 cm3 what is the volume of the bigger sphere?
322
2
3
384848148
8
1cmvv
v
cm
9.) If the ratio of radii of two similar cylinders is 3:5
a.) Ratio of corresponding Perimeters?_______
b.) Ratio of areas?______
c.) Ratio of volumes?______
If the volume of the smaller sphere is 54 cm3 what is the volume of the bigger sphere?
Sample Problem:Find the area and volume of the sphere with a radius of 10 cm
a.) Area=4πr2 b.) Volume= =4π(10)2
=4π(100) =400π cm2
3
4000
)1000(3
4
)10(3
43
4
3
3
r
10. Find the area and volume of the sphere with a radius of 5
a.) Area=_______
b.) Volume=_______
Sample problem A regular pyramid has a base edge of 3cm and volume
135cm3 Find h.Volume=1/3Bh
135=1/3(9)h
135= 3h
3 3
45 cm=h 3 cm
3 cm
h
11. A regular pyramid has a base edge of 3cm and volume 100cm3 Find h.h=________
3 cm
3 cm
h
Sample problem A cone has radius 8 and height 6. Find the volume. Slant
heightV=1/3Bh
=1/3πr2h
=1/3π(8)2(6)
=1/3π64(6)
=1/3π384
=384/3π
=128π
H=6
r=8
L=slant height
62+82=l2
36+64=l2
100=l2
10=l
(2x3)2+(2x4)2=l2
3-4-5 l=5x2=10
12. A cone has radius 12 and height 9. Find the volume. Slant height
V=_______
H=9
r=12
L=slant height
=__________
Sample problem A cone has radius 8 and height 6. Find Total area.
H=6
r=8
l=slant height
62+82=l2
36+64=l2
100=l2
10=l
(2x3)2+(2x4)2=l2
3-4-5 l=5x2=10
TA=LA+B
=πrl+πr2
=π(8)(10)+π82
=80π+64π
=144π units2
13. A cone has radius 12 and height 9. Find Total area.
H=9
r=12
l=slant height
=_____
TA=_______
Sample problem A cylinder has a radius 6cm and height 4cm. Find
total area.TA=LA+2B
=ph+2B
=(2πr)h+2πr2
=2π(6)(4)+2π62
=48π+72π
=120π cm2
R=6
h=4
14. A cylinder has a radius 8cm and height 3cm. Find total area.
TA=_________
R=8
h=3
Sample problem. A cylinder has a radius 6cm and height 4cm. Find
volume.V=Bh
=πr2h
=π62(4)
=π36(4)
=144π cm3 R=6
h=4
15. A cylinder has a radius 8cm and height 3cm. Find volume.
V=________
R=8
h=3