1. Surface area and Volume Good luck. No work=No credit.
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.

2. Part 1: Matching 1.)prism A.) Type of solid. 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.

3. Sample problem for 1 and 2: Find the volume and total area of a cube with edge 2k.
Volume=Bh
=(2k2k)(2k)
=8k3 units3
Total Area=LA+2B
=ph+2B
=8k(2k)+2(2k)(2k)
=16k2+8k2
=24k2 units2 2k 2k 2k 2k 2k 2k 2k

4. 1.) Find the volume of this rectangular prism10
Bases 4 3

5. 2.) Find the Lateral area and Total area of this rectangular prism10
Bases 4 3

6. 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 units2
20cm
13cm
5cm
12cm

7. Sample problem A right triangular prism has height 10 and base edges 3, 4, 5. TA?
Total area=_______
10cm
5cm
3cm
4cm

8. Sample problem for 4. Find the Lateral Area of a triangular prism
LA=ph
=(8+8+6)(12)
=22(12)
=264 units2 12 8 8 6

9. 4. Find Lateral Area of the triangular prism20 16 16 12

10. 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.
LA=ph
180= p(9)
p=20 ml

11. Find the missing variable for each prism.
7.) LA=729 p=
h=9

12. Sample problem: Find the volume of a Cylinder
√H = √9
H = 3
V=Bh
=πr2h
=π(2)2(3)
=12π ft.3
5 ft
h=___ ft
4 ft
d=______
r=______
h=______

13. 8. Find the volume of a Cylinder
25 ft
h=___ ft
24 ft
d=______
r=______
h=______

14. 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?

15. 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?

16. Sample Problem: Find the area and volume of the sphere with a radius of 10 cm
a.) Area=4πr b.) Volume=
=4π(10)2
=4π(100)
=400π cm2

17. 10. Find the area and volume of the sphere with a radius of 5
a.) Area=_______
b.) Volume=_______

18. 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
45 cm=h h
3 cm
3 cm

19. 11. A regular pyramid has a base edge of 3cm and volume 100cm3 Find h.

20. Sample problem A cone has radius 8 and height 6. Find the volume
Sample problem A cone has radius 8 and height 6. Find the volume. Slant height
V=1/3Bh
=1/3πr2h
=1/3π(8)2(6)
=1/3π64(6)
=1/3π384
=384/3π
=128π
L=slant height
62+82=l2
36+64=l2
100=l2
10=l
(2x3)2+(2x4)2=l2
l=5x2=10
H=6
r=8

21. 12. A cone has radius 12 and height 9. Find the volume. Slant height
L=slant height
=__________
H=9
r=12

22. Sample problem A cone has radius 8 and height 6. Find Total area.
TA=LA+B
=πrl+πr2
=π(8)(10)+π82
=80π+64π
=144π units2
l=slant height
62+82=l2
36+64=l2
100=l2
10=l
(2x3)2+(2x4)2=l2
l=5x2=10
H=6
r=8

23. 13. A cone has radius 12 and height 9. Find Total area.
l=slant height
=_____
H=9
r=12

24. Sample problem A cylinder has a radius 6cm and height 4cm
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
h=4
R=6

25. 14. A cylinder has a radius 8cm and height 3cm. Find total area.

26. Sample problem. A cylinder has a radius 6cm and height 4cm. Find volume.
V=Bh
=πr2h
=π62(4)
=π36(4)
=144π cm3
h=4
R=6

27. 15. A cylinder has a radius 8cm and height 3cm. Find volume.