11.1 practice a€¦ · of 14 centimeters. in exercises 4–9, ... geometry copyright © big ideas...

Copyright © Big Ideas Learning, LLC Geometry All rights reserved. Resources by Chapter

375

11.1 Practice A

Name _________________________________________________________ Date __________

In Exercises 1–4, find the indicated measure.

1. radius of a circle with a circumference of 42 metersπ

2. circumference of a circle with a radius of 27 feet

3. circumference of a circle with a diameter of 15 inches

4. diameter of a circle with circumference 39 centimeters

5. Maple trees suitable for tapping for syrup should be at least 1.5 feet in diameter. You wrap a rope around a tree trunk, then measure the length of the rope needed to wrap one time around the trunk. This length is 4 feet 2 inches. Explain how you can use this length to determine whether the tree is suitable for tapping.

In Exercises 6–8, find the arc length of AB.

6. 7. 8.

In Exercises 9 and 10, find the perimeter of the region.

9. 10.

In Exercises 11 and 12, convert the angle measure.

11. Convert 60° to radians. 12. Convert 54π radians to degrees.

13. A carousel has a diameter of 50 feet. To the nearest foot, how far does a child seated near the outer edge travel when the carousel makes 8 revolutions?

60°P

6 cm

A

B 150° P

18 in.

A

B

30°

P28 ft

C

AB

4 mm

28 in.

28 in.

6 in. 6 in.

50 ft

Carosel

Geometry Copyright © Big Ideas Learning, LLC Resources by Chapter All rights reserved. 376

11.1 Practice B

Name _________________________________________________________ Date _________

In Exercises 1 and 2, find the indicated measure.

1. exact diameter of a circle with a circumference of 36 meters

2. exact circumference of a circle with a radius of 5.4 feet

3. Find the circumference of a circle inscribed in a square with a side length of 14 centimeters.

In Exercises 4–9, use the diagram of circle D with EDF FDG∠ ≅ ∠ to find the

indicated measure.

4. mEFG

5. mEHG

6. arc length of EFG

7. arc length of EHG

8. mEHF

9. arc length of FEG


10. mAB 11. circumference of F 12. radius of J

In Exercises 13 and 14, convert the angle measure.

13. Convert 105° to radians. 14. Convert 5

6

π radians to degrees.

15. The chain of a bicycle travels along the front and rear sprockets, as shown in the figure. The circumferences of the rear sprocket and the front sprocket are 12 inches and 20 inches, respectively.

a. How long is the chain? Round your answer to the nearest tenth.

b. On a chain, the teeth are spaced in 12

-inch intervals.

About how many teeth are there on this chain?

H

E G

F

80°

D

7 m

10 in.160° 185°

10 in.

23.88 in.

C12 in. A

B

F46.75 ft

D

E

290° J

19.71 cmH

G55°


11.2 Practice A

Name _________________________________________________________ Date _________


1. area of a circle with a radius of 6.8 feet

2. area of a circle with a diameter of 19.2 centimeters

3. radius of a circle with an area of 1017.9 square meters

4. diameter of a circle with an area of 707 square inches

5. About 1.2 million people live in a region with a 6-mile radius. Find the population density in people per square mile.

6. A region with a 15-mile diameter has a population density of about 5000 people per square mile. Find the number of people who live in the region.

In Exercises 7–10, find the areas of the sectors formed by JLK.∠

7. 8. 9. 10.

11. Find the area of .H 12. Find the area of .M

In Exercises 13–15, find the area of the shaded region.

13. 14. 15.

16. The diagram shows the coverage of a security camera outside a building. A new security camera is installed in the same position that doubles the radius of the coverage area. How does this affect the coverage area? Explain.

7 ft50°

M

L

J

K

13 in.

125° ML

J

K

1 m140°

M

L

J K 8 cm45°

ML J

K

70°

F

A = 156.38 yd2

E

H

G

40°J

K

A = 11.17 m2

L

M

8 ft17 ft

3 mm

17 mm

10 cm

10 cm

13000°°

40 ft


381

11.2 Practice B

4 in.

5 in.

4 in..

5 in.5 in

30°

Name _________________________________________________________ Date __________


1. area of a circle with a radius of 6.75 inches

2. area of a circle with a diameter of 310 mile

3. radius of a circle with an area of 63.7 square kilometers

4. diameter of a circle with an area of 1040.62 square yards

5. About 150,000 people live in a circular region with a population density of about 1578 people per square mile. Find the radius of the region.

6. About 1.75 million people live in a circular region with a population density of about 5050 people per square mile. Find the radius of the region.

In Exercises 7–10, find the areas of the sectors formed by JLK.∠

7. 8. 9. 10.

11. Find the radius of .H 12. Find the radius of .M


13. 14. 15.

16. A piece of cake is a sector of a cylinder as shown. What is the volume of the piece of cake?

0.4 m

M

J K

L

127°J

K

39°2.9 cm

M

L

J

K

ML 77°

yd123

88°

F

A = 4.8 cm2

E

H

GA = 1.05 ft2

L

J

K

M

25°

5 m 180°

7 ft

45°

6 in.

4 in.

J

K

M113°

in.58

L


385

11.3 Practice A

Name _________________________________________________________ Date __________

In Exercises 1–4, find the area of the kite or rhombus.

1. 2. 3. 4.

In Exercises 5–8, find the measure of a central angle of a regular polygon with the given number of sides. Round answers to the nearest tenth of a degree, if necessary.

5. 9 sides 6. 16 sides 7. 20 sides 8. 28 sides

In Exercises 9–12, find the given angle measure for regular hexagon ABCDEF.

9. m∠CGD 10. m∠CGH

11. m∠HCG 12. m∠EGC

In Exercises 13–17, find the area of the regular polygon.

13. 14. 15.

16. a pentagon with an apothem of 7 centimeters

17. a decagon with a radius of 20 meters

18. Use the figure of the gazebo floor.

a. An arm rail is built around the perimeter of the gazebo. What is the length of the arm rail?

b. A container of wood sealer covers 200 square feet. How many containers of sealer do you need to cover the entire floor of the gazebo? Explain your reasoning.

15

27

12

9

27

16

6

10

A B

GCF

E D

H

3.5 3

14

10

12 ft


11.3 Practice B

Name _________________________________________________________ Date _________

In Exercises 1–4, find the area of the kite or rhombus.

1. 2. 3. 4.

In Exercises 5–8, find the given angle measure for regular heptagon ABCDEFG. Round your answer to the nearest tenth of a degree, if necessary.

5. m∠BHC 6. m∠BHI

7. m∠IBH 8. m∠EHB


9. 10. 11.

12. The area of a kite is 384 square feet. One diagonal is three times as long as the other diagonal. Find the length of each diagonal.

13. The area of a rhombus is 484 square millimeters. One diagonal is one-half as long as the other diagonal. Find the length of each diagonal.

14. You are laying concrete around a gazebo that is a regular octagon with a radius of 8 feet. The concrete will form a circle that extends 15 feet from the vertices of the octagon.

a. Sketch a diagram that represents this situation.

b. What is the area of the concrete to the nearest square foot?

15. The perimeter of a regular 11-gon is 16.5 meters. Is this enough information to find the area? If so, find the area and explain your reasoning. If not, explain why not.

17.5

32.68.9

6.225

10.1

24

20

E D

F

G

A

B

CH I

6

4

10

45°


11.4 Practice A

Name _________________________________________________________ Date _________

In Exercises 1–3, tell whether the solid is a polyhedron. If it is, name the polyhedron.

1. 2. 3.

In Exercises 4–6, describe the cross section formed by the intersection of the plane and the solid.

4. 5. 6.

In Exercises 7–9, sketch the solid produced by rotating the figure around the given axis. Then identify and describe the solid.

7. 8. 9.

10. Is the block shown a polyhedron? Explain your reasoning.

11. Sketch a cube. Is it possible for a cross section of a cube to be a square? Explain your reasoning. If so, describe or sketch two different ways in which the plane could intersect the solid.

12. Consider the rectangular prism in Exercise 1. The length of the prism is 4 inches, the width is 2 inches, and the height is 2 inches.

a. What is the perimeter of the cross section?

b. What is the area of the cross section?

9 9

5

5

2

2 4

6


391

11.4 Practice B

Name _________________________________________________________ Date __________

In Exercises 1–3, describe the cross section formed by the intersection of the plane and the solid.

1. 2. 3.

In Exercises 4–6, sketch the solid produced by rotating the figure around the given axis. Then identify and describe the solid.

4. 5. 6.

7. Which of the parts shown are polyhedrons? Explain your reasoning.

8. Sketch the composite solid produced by rotating the composite figure around the given axis. Then identify and describe the composite solid.

9. A cone with a height of 6 inches and radius of 4 inches is sliced in half by a horizontal plane, creating a circular cross section with a radius of 2 inches. Each piece is then sliced in half by a vertical plane, as shown.

a. Describe the shape formed by each cross section.

b. What are the perimeters and areas of the cross sections?

c. Suppose the horizontal plane is tilted, slicing the original cone as shown at the right. Is the cross section a circle? If it is not, describe how it is different from a circle and sketch the cross section.

6 6

6

6

3

4

2

9

9

3 in.

32

6

8


395

11.5 Practice A

Name _________________________________________________________ Date __________

In Exercises 1 and 2, find the volume of the prism.

1. 2.

In Exercises 3 and 4, find the volume of the cylinder.

3. 4.

5. A cylindrical container with a radius of 12 centimeters is filled to a height of 6 centimeters with coconut oil. The density of coconut oil is 0.92 gram per cubic centimeter. What is the mass of the coconut oil to the nearest gram?

In Exercises 6 and 7, find the missing dimension.

6. 3Volume 240 m= 7. 3Volume 1244 in.=

In Exercises 8 and 9, find the area of the base of the rectangular prism with the given volume and height. Then give a possible length and width.

8. 396 ft , 8 ftV h= = 9. 3144 cm , 6 cmV h= =

10. The prisms are similar. Find the volume 11. Find the volume of of Prism B. the composite solid.

12. A cylindrical swimming pool is approximately 12 feet wide and 4 feet deep. About how many gallons of water does the swimming pool contain? Remember that 1 cubic foot is approximately 7.48 gallons.

3 in.

4 in.7 in.

9 cm8 cm

12 cm

5 ft

4 ft

6 yd

10 yd

5 ms

8 m

t

6 in.

8 m

Prism A

V = 800 m3

Prism B

6 m

5 cm

7 cm

9 cm

4 cm

2 cm1 cm


11.5 Practice B

Name _________________________________________________________ Date _________

In Exercises 1 and 2, find the volume of the prism.

1. 2.

In Exercises 3 and 4, find the volume of the cylinder.

3. 4.

5. A cylindrical container with a radius of 8 centimeters is filled to a height of 10 centimeters with sulfuric acid. The density of sulfuric acid is 1.84 grams per cubic centimeter. What is the mass of the sulfuric acid to the nearest gram?

In Exercises 6 and 7, find the missing dimension.

6. 3Volume 120 ft= 7. 3Volume 254.5 m=

In Exercises 8 and 9, find the area of the base of the rectangular prism with the given volume and height. Then give a possible length and width.

8. 3216 yd , 12 ydV h= = 9. 3448 in. , 14 in.V h= =

10. The cylinders are similar. Find the volume 11. Find the volume of the composite solid. of Cylinder B.

12. An aquarium shaped like a rectangular prism has a length of 24 inches, a width of 12 inches, and a height of 18 inches. You fill the aquarium half full with water. When you submerge a rock in the aquarium, the water level rises 0.5 inch. Find the volume of the rock.

6 ft

12 ft8 ft

2.4 m

3.2 m3 m

1.6 m

32.6 in.

12.5 in.

12 cm

11.8 cm

10 ft

6 ftq

9 m

r

Cylinder A

V = 112 in.3

4 in.

Cylinder B

π

6 in.

5 ft5 ft

5 ft


11.6 Practice A

Name _________________________________________________________ Date _________

In Exercises 1–3, find the volume of the pyramid.

1. 2. 3.


4. A pyramid with a square base has a volume of 320 cubic centimeters and a height of 15 centimeters. Find the side length of the square base.

5. A pyramid with a rectangular base has a volume of 60 cubic feet and a height of 6 feet. The width of the rectangular base is 4 feet. Find the length of the rectangular base.

6. A pyramid with a triangular base has a volume of 80 cubic meters and a base area of 20 square meters. Find the height of the pyramid.

In Exercises 7 and 8, the pyramids are similar. Find the volume of Pyramid B.

7. 8.

In Exercises 9–11, find the volume of the composite solid.

9. 10. 11.

12. The Pyramid Arena in Memphis, Tennessee is about 98 meters tall and has a square base with a side length of about 180 meters. A prism-shaped building has the same square base as the Pyramid Arena. What is the height of the building if it has the same volume as the Pyramid Arena?

15 in.

6 in.

Pyramid A

Pyramid B

V = 500 in.3

4 mm

16 mm

Pyramid B

Pyramid A

V = 16 mm3

8 yd

8 yd

9 yd

8 yd

6 m

5 m

10 m

16.5 m

10 cm

10 cm12 cm

7 ft

4 ft

9 ft

16 m

10 m

9 m

13 in.

15 in.


401

11.6 Practice B

Name _________________________________________________________ Date __________

In Exercises 1–3, find the volume of the pyramid.

1. 2. 3.


4. A pyramid with a square base has a volume of 119.07 cubic meters and a height of 9 meters. Find the side length of the square base.

5. A pyramid with a hexagonal base has a volume of about 1082.54 cubic inches and a base area of about 259.81 square inches. Find the height of the pyramid.

In Exercises 6 and 7, the pyramids are similar. Find the volume of Pyramid B.

6. 7.

In Exercises 8–10, find the volume of the composite solid.

8. 9. 10.

11. The volume of the pyramid shown is 48 3 cubic meters. Find the value of x.

8 cm

10 cm

4 ft

7 ft

5 yd

16 yd

10 cm

24 cm

Pyramid A

V = 160 cm

Pyramid BPyramid A

Pyramid B

5.2 yd20.8 yd

V = 2059.2 yd3

8 cm

13 cm

5 cm

5 cm

16 in.

18 in.

20 in.10 m

10 m

9 m

x x

9 m

x


405

11.7 Practice A

Name _________________________________________________________ Date __________

In Exercises 1 and 2, find the surface area of the right cone.

1. 2.

In Exercises 3 and 4, find the volume of the cone.

3. 4.

In Exercises 5 and 6, the cones are similar. Find the volume of Cone B.

5. 6.

In Exercises 7 and 8, find the volume of the composite solid.

7. 8.

9. A cone has height h and a base with radius r. You want to change the cone so its volume is tripled. What is the new height if you only change the height? What is the new radius if you only change the radius? Explain.

10. A snack stand serves shaved ice in cone-shaped containers and cylindrical containers. Which container gives you more shaved ice for your money? Explain.

6 ft

14 ft

10 m

18 m

5 cm

8 cm

2 in.

4 in.

Cone ACone B

V = 72 mm3π

9 mm 12 mm

Cone ACone B

V = 28 in.3π

4 in. 2 in.

6 in. 6 in.

$3.25$4.75

4 in.4 in.

15 in.

7 in.

4 in.

4 cm

4 cm

4 cm


11.7 Practice B

Name _________________________________________________________ Date _________

In Exercises 1 and 2, find the surface area of the right cone.

1. 2.

In Exercises 3 and 4, find the volume of the cone.

3. 4.

In Exercises 5 and 6, the cones are similar. Find the volume of Cone B.

5. 6.


7. 8.

9. A cone has height h and a base with radius r. You want to change the cone so its volume is halved. What is the new height if you only change the height? What is the new radius if you only change the radius? Explain.

10. During a chemistry lab, you use a funnel to pour a solvent into a flask. The radius of the funnel is 4 centimeters and its height is 12 centimeters. You pour the solvent into the funnel at a rate of 60 milliliters per second and the solvent flows out of the funnel at a rate of 40 milliliters per second. How long will it be before the funnel overflows? (Remember that 1 milliliter is equal to 1 cubic centimeter.)

20 yd

7 yd

15 mm

8.6 mm

11 in.

14 in.

6 cm4 cm

Cone A

V = 700 ft3π

Cone B

6 ft10 ft

Cone A

Cone B

V = 24 m3π

6 m 14 m

2.8 cm

2.8 cm

2.8 cm

6 in.

6 in.

8 in.

8 in.

10 in.


11.8 Practice A

Name _________________________________________________________ Date _________

In Exercises 1–3, find the surface area of the sphere.

1. 2. 3.


4. the radius of a sphere with a surface area of 36 square metersπ

5. the diameter of a sphere with a surface area of 81 square yardsπ

In Exercises 6–8, find the volume of the sphere.

6. 7. 8.

In Exercises 9 and 10, find the volume of the sphere with the given surface area.

9. 2Surface Area 4 in.π= 10. 2Surface Area 676 kmπ=


11. 12.

13. Find the surface area and volume of the solid produced by rotating the figure at the right around the given axis.

14. A sphere is inscribed in a cube with a volume of 8 cubic yards. What is the surface area of the sphere? Explain your reasoning.

15. In 2000, the International Table Tennis Federation changed the official diameter of a table tennis ball from 38 millimeters to 40 millimeters. Without calculating surface areas and volumes, determine how the surface area and volume of the ball changed. Explain your reasoning. Find the surface areas and volumes to check your answer.

2 in. 10 mm

C = 8 ftπ

3 ft 30 cm 10.8 m

18 cm

9 cm6 ft

15 ft

4 m

4 m


411

11.8 Practice B

Name _________________________________________________________ Date __________

In Exercises 1–3, find the surface area of the sphere or hemisphere.

1. 2. 3.


4. the radius of a sphere with a surface area of 100π square centimeters

5. the diameter of a sphere with a surface area of 6.25π square inches

In Exercises 6–8, find the volume of the sphere or hemisphere.

6. 7. 8.

In Exercises 9 and 10, find the volume of the sphere with the given surface area.

9. 2Surface Area 144 ftπ= 10. 2Surface Area miπ=


11. 12.

13. The diameter of a spherical balloon shrinks to one-half of its original size. Describe how the surface area and volume of the balloon change.

14. A museum has two spherical cannonballs on display. Each cannonball is made of a type of iron that weighs about 463 pounds per cubic foot.

a. The diameter of the smaller cannonball is 1 inch less than the diameter of the larger cannonball. Can you determine how much less the smaller cannonball weighs than the larger cannonball? Explain your reasoning.

b. The smaller cannonball displaces 33.5 cubic inches of water when dropped in a bucket full of water. To the nearest pound, how much less does the smaller cannonball weigh than the larger cannonball?

6 m

3.5 yd C = 9 in.π

9 ft 13 cm

C = 20 mπ

9 yd14 yd 2 in.

2 in.

4 in.

11.1 practice a€¦ · of 14 centimeters. in exercises 4–9, ... geometry copyright © big ideas...

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