chapter 11 practice test #1 - m2...

Chapter 11 Practice Test #1

Class Name : M29 Geometry - 2019-20 Term 2 Instructor Name : Mr. Beckey

Student Name : _____________________ Instructor Note :

1. In each figure below, a plane passes through a geometric solid as shown.For each figure, choose the shape of the cross section formed.

2. Each region below is being rotated about the line

Figure Cross section

(a)

(b)

(c)

© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 11 Pr ac t i ce T es t #1 / 19

2. Each region below is being rotated about the line .For each region, identify the solid generated by the rotation.

3. Find the volume of the rectangular prism.

4. Find the volume of the oblique rectangular prism with length , width , and height .

l

Region Solid

(a)

l

(b)

l

(c)l

9 cm 8 cm 9 cm

5 in

5 in

5 in


4. Find the volume of the oblique rectangular prism with length , width , and height .

5. Find the volume of this triangular prism.

Be sure to include the correct unit in your answer.

6. The radius of a cylindrical construction pipe is . If the pipe is long, what is its volume?

Use the value for , and round your answer to the nearest whole number.Be sure to include the correct unit in your answer.

7. Find the volume of an oblique cylinder with a base diameter of and a height of

9 cm 8 cm 9 cm

2 ft 23 ft

3.14 π

6 cm 26 cm

9 cm

8 cm9 cm

5 yd

10 yd

9 yd

23 ft

2 ft


7. Find the volume of an oblique cylinder with a base diameter of and a height of .

Use the value for , and round your answer to the nearest whole number.


8.

Conversion facts for volume and capacity

cubic yard gallons

cubic foot gallons

cubic inches gallon

Note that means "is approximately equal to".

For this problem, treat as if it were .

A water tower has a volume of .Use the table of conversion facts to find out how many gallons of water it would take to completely fill the watertower.

Round your answer to two decimal places.

__________________

9. Find the volume of the solid.

6 cm 26 cm

3.14 π

1 yd3 ≈ 201.97 gal

1 ft3 ≈ 7.48 gal

231 in3 = 1 gal

≈≈ =

1896 yd3

gal

26 cm

6 cm


9. Find the volume of the solid.

10. The solid below is made from cubes.Find its volume.

11. A company makes wax candles shaped like rectangular prisms. Each candle is long, wide, and

tall. If the company used of wax, how many candles did they make?

12. A solid object in the shape of a cylinder is shown below.

5 cm 2 cm

12 cm 5040 cm 3

11 mm

4 mm6 mm

2 mm6 mm

5 mm6 mm

1 yd



It has a radius of and a height of .

If its mass is , what is its density?

Use the value for .Round your answer to the nearest hundredth. Do not round any intermediate steps.Be sure to include the correct unit in your answer.

13. Answer the questions below.

Give exact integer or decimal answers.Be sure to include the correct units in your answers.

(a) An object has a density of and a volume of .

What is the mass of the object?

Mass

(b) Another object has a density of and a mass of .

What is the volume of the object?

Volume

14. A solid object in the shape of a rectangular prism is shown below.

3 m 8 m18.3 kg

3.14 π

24g

cm 3 60 cm 3

=

18g

cm 3 720 g

=

8 m 3 m



If its mass is , what is its density?

Give an exact integer or decimal answer.Be sure to include the correct unit in your answer.

15. Find the volume of this rectangular pyramid.


16. Find the volume of a cone with a base diameter of and a height of

18.2 kg

12 yd 11 yd

5 m4 m

7 m

7 cm 3 cm

8 cm


16. Find the volume of a cone with a base diameter of and a height of .

Use the value for , and do not do any rounding.Be sure to include the correct unit in your answer.

17. The radius of a sphere is . Calculate the sphere's surface area .

Use the value for , and round your answer to the nearest tenth.

18. The radius, , of a sphere is . Calculate the sphere's volume, .

Use the value for , and round your answer to the nearest tenth. (Do not round any intermediatecomputations.)

19. Check all statements that are true.

12 yd 11 yd

3.14 π

R 3.8 cm A

3.14 π

R 9.4 m V

3.14 π

12 yd

11 yd


19. Check all statements that are true.

In spherical geometry, through any point not on a given line there are no lines parallel to the given line.

In spherical geometry, the sum of the angle measures of a triangle is equal to .In spherical geometry, a triangle can have two right angles.In Euclidean geometry, some quadrilaterals are parallelograms.In both Euclidean and spherical geometry, every pair of lines must intersect.None of these are true.

20. For each pair of solids, determine whether they are similar.

180 °


20. For each pair of solids, determine whether they are similar.If they are, give the scale factor of Solid 1 to Solid 2 in simplest form.

(Note: The figures are not drawn to scale.)

21. A designer builds a model of a truck. The finished model is exactly the same shape as the original, but

(a) The solids are right rectangular pyramids.Their lengths, widths, and heights are shown. Similar

6 cm

4 cm2 cm

21 cm

14 cm

7 cm

Solid 1 Solid 2

Scale =factor

Not similar

(b) The solids are right rectangular prisms.Their lengths, widths, and heights are shown. Similar

15 cm

14 cm5 cm

27 cm

16 cm9 cm

Solid 1 Solid 2

Scale =factor

Not similar

(c) The solids are right cones.Their heights and base diameters are shown. Similar

6 cm

2 cm

15 cm

5 cmSolid 1 Solid 2

Scale =factor

Not similar


21. A designer builds a model of a truck. The finished model is exactly the same shape as the original, but

smaller. The scale factor is .

(a) Find the ratio of the surface area of the model to the surface area of the original.

(b) Find the ratio of the volume of the model to the volume of the original.

(c) Find the ratio of the height of the model to the height of the original.

Write these ratios in the format m:n.

22. Two similar cylinders have diameters as shown below.(Note: The figures are not drawn to scale.)

(a) If the height of the cylinder on the left is , find the height of the cylinder on the right.

(b) If the volume of the cylinder on the left is , find the volume of the cylinder on the right.

(c) If the surface area of the cylinder on the left is , find the surface area of the cylinder on the right.

23. A map of a city shaped like a rectangle is given below on a grid. In the city's population was

:2 11

14 m

686 m3

588 m2

2011 759,000

6 m7 m


23. A map of a city shaped like a rectangle is given below on a grid. In , the city's population was

people. What was the population density in ?


24. Answer the questions below.

Give exact integer or decimal answers.Be sure to include the correct units in your answers.

(a) An object has a mass of and a volume of .What is the density of the object?

Density

(b) Another object has a volume of and a density of .


Mass


2011 759,0002011

625 g 125 cm 3

=

80 cm 3 25g

cm 3

=

xx

10 20 30 40 50 60 70

yy

10

20

30

40

50

60

70

0

kmkm

kmkm



If its density is , what is its mass?

Give an exact integer or decimal answer.Be sure to include the correct unit in your answer.


It has a radius of and a height of .

If its density is , what is its mass?

Use the value for .Round your answer to the nearest hundredth. Do not round any intermediate steps.Be sure to include the correct unit in your answer.

18.4 kg

m3

2.6 cm 4 cm

28g

cm 3

3.14 π

2 m

2 m

2 m

4 cm 2.6 cm


Chapter 11 Practice Test #1 Answers for class M29 Geometry -2019-20 Term 2

1.

2.

Figure Cross section

(a)

(b)

(c)


2.

3.

4.

5.

6.

7.

8.

9.

Region Solid

(a)

l

(b)

l

(c)l

125 in3

648 cm 3

225 yd3

289 ft3

735 cm 3

382,935.12 gal

192 mm 3

3 © 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 11 Pr ac t i ce T es t #1 / 19

10.

11. candles

12. Density

13.

(a) An object has a density of and a volume of .


Mass

(b) Another object has a density of and a mass of .

What is the volume of the object?

Volume

14. Density

15.

16.

17.

18.

19.

30 yd3

42

=0.08kg

m3

24g

cm 3 60 cm 3

= 1440 g

18g

cm 3 720 g

= 40 cm 3

=0.13 kg

m3

56 cm 3

414.48 yd3

=A 181.4 cm 2

=V 3477.4 m3


19.

In spherical geometry, through any point not on a given line there are no lines parallel to the given line.

In spherical geometry, the sum of the angle measures of a triangle is equal to .In spherical geometry, a triangle can have two right angles.In Euclidean geometry, some quadrilaterals are parallelograms.In both Euclidean and spherical geometry, every pair of lines must intersect.None of these are true.

20.

180 °


20.

21.

(a)

(b)

(c)

22.

(a) The solids are right rectangular pyramids.Their lengths, widths, and heights are shown. Similar

6 cm

4 cm2 cm

21 cm

14 cm

7 cm

Solid 1 Solid 2

Scale =factor2

7

Not similar

(b) The solids are right rectangular prisms.Their lengths, widths, and heights are shown. Similar

15 cm

14 cm5 cm

27 cm

16 cm9 cm

Solid 1 Solid 2

Scale =factor

Not similar

(c) The solids are right cones.Their heights and base diameters are shown. Similar

6 cm

2 cm

15 cm

5 cmSolid 1 Solid 2

Scale =factor2

5

Not similar

:4 121

:8 1331

:2 11


22.

(a) Height:

(b) Volume:

(c) Surface Area:

23. Population density:

24.

(a) An object has a mass of and a volume of .What is the density of the object?

Density

(b) Another object has a volume of and a density of .


Mass

25. Mass

26. Mass

12 m

432 m3

432 m2

460 people

km2

625 g 125 cm 3

= 5g

cm 3

80 cm 3 25g

cm 3

= 2000 g

=147.2 kg

=2377.36 g


chapter 11 practice test #1 - m2...

Documents