Chapter 12 Test: Instructions: Leave all answers in terms of π and reduce all fractions. Surface...

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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:

Transcript of Chapter 12 Test: Instructions: Leave all answers in terms of π and reduce all fractions. Surface...

Page 1: 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:

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:

Page 2: 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.

Page 3: 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:

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

Page 4: 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:

1.) Find the volume of this rectangular prism

10

4

3

Bases

Page 5: 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:

2.) Find the Lateral area and Total area of this rectangular prism

10

4

3

Bases

Page 6: 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:

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

Page 7: 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:

Sample problem A right triangular prism has height 10 and base

edges 3, 4, 5. TA?Total area=_______

3cm5cm

4cm

10cm

Page 8: 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:

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

Page 9: 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:

4. Find Lateral Area of the triangular prism

16

16

12

20

Page 10: 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:

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

Page 11: 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:

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

Page 12: 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:

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

Page 13: 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:

8. Find the volume of a Cylinder

25 ft

24 ft

d=______r=______h=______

h=___ ft

Page 14: 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:

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

Page 15: 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:

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?

Page 16: 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:

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

Page 17: 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:

10. Find the area and volume of the sphere with a radius of 5

a.) Area=_______

b.) Volume=_______

Page 18: 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:

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

Page 19: 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:

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

3 cm

3 cm

h

Page 20: 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:

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

Page 21: 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:

12. A cone has radius 12 and height 9. Find the volume. Slant height

V=_______

H=9

r=12

L=slant height

=__________

Page 22: 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:

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

Page 23: 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:

13. A cone has radius 12 and height 9. Find Total area.

H=9

r=12

l=slant height

=_____

TA=_______

Page 24: 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:

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

Page 25: 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:

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

TA=_________

R=8

h=3

Page 26: 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:

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

Page 27: 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:

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

V=________

R=8

h=3