distance: midpoint: x y y y 1 x 2 y § 2 1 2 1 2 x x 1. (-5

Geometry: Unit 11 Warm-Ups Name: _________________________

Cumulative Review Date: _____________

Monday, January 9th: Calculate the distance, midpoint, and slope between each set of points.

2122

12 yyxx 12

12

xx

yy

2,

21212 yyxx

Distance: Midpoint: Slope:

1. (-5, 6) and (-5, -9) 2. (4, 8) and (-2, 8)

Distance: _______

Midpoint: _______

Slope: __________

Distance: _______

Midpoint: _______

Slope: __________

3. (2, -6) and (5, 2) 4. (9 -3) and (-9, 4)

Distance: _______

Midpoint: _______

Slope: __________

Distance: _______

Midpoint: _______

Slope: __________

VOCABULARY REVIEW:

Geometry Name: ____________________________________

Unit 11 Warm-Ups Date: Tuesday, January 10th

1.

2.

Calculate the lateral area, total area, and volume of the given solids.

1.2cm

1.2cm

1.2cm

Lateral Area:

Total Area:

9m

4m

8m

Cumulative Review: Determine the value of x and the missing segments. Label Diagrams!!

3.) AC = 6x AB = 10 BC = 2x+2

4.) AC = 30 AB = 5x+2 BC = 10x-2

5.) AC = x+8 AB = 6 BC = 2x-1

P:

B:

H:

Volume:

Lateral Area:

Total Area:

P:

B:

H:

Volume:

A B C

A B C

A B C

x =

AC =

BC =

x =

AB =

BC =

x =

AC =

BC =

Geometry Name: ____________________________________

Unit 11 Warm-Ups Date: Wednesday, January 11th

1.

2.

Figure Volume Area

Cumulative Review: Determine the value of x and the missing angles or segments.

15in

17in

12m

18m20m

x =

mABD =

mABC =

x =

mABD =

mABC =

5. B is the midpoint of AC, AB = x + 4 and BC = 2x – 5. Find x, AB, BC, and AC.

x =

AB=

BC=

AC=

Lateral Area:

Total Area:

P:

B:

H:

L:

Volume:

Lateral Area:

Total Area:

P:

B:

H:

L:

Volume:

3.) a||b 4.) c||d 5.) e||f

Complete the following definitions.

6. Points on the same line are called .

7. Points that lie on the same plane are called .

8. Lines that lie in the same plane and never intersect are called .

9. An angle with measure of more than 0 and less than 90 is a angle.

10. angles are two angles who measures sum to 180.

11. angles are two angles who measures sum to 90.

Geometry Name: ____________________________________

Unit 11 Warm-Ups Date: Thursday, January 12th

1.

2.

Figure Volume Area

Cumulative Review: Use the properties of parallel lines to find x.

49m

14m

34cm

30cm

9x+23

11x-15

10x-15

5x+80

3x+12

5x+8

B:

H:

r:

Volume:

Lateral Area:

Total Area:

B:

R:

H:

L:

Volume:

Lateral Area:

Total Area:

3.) 4.) 5.)

Classify: Classify: Classify:

Largest Angle: Longest Side: Largest Angle:

Smallest Angle: Shortest Side: Smallest Angle:

Geometry Name: ____________________________________

Unit 11 Warm-Ups Date: Friday, January 13th

1.

2.

Figure Volume Area

Cumulative Review: Classify the triangle by it’s sides or angles. State which side or angles will be the largest and the smallest.

16m

24cm

Cumulative Review: Find the value of x.

6.) 7.) 8.)

x = x = x =

Geometry Name: ____________________________________

Unit 11 Warm-Ups Date: Tuesday, January 17th

1.Calculate the lateral area, total area, and volume. Use 3.14.

49m

14m

B:

H:

r:

Volume:

Lateral Area:

Total Area:

2. A soup company is in the process of redesigning their can for a new line of products. The can

is to have a height of 4 inches and a radius of 2 inches. Round to the nearest tenth.

a. Sketch the solid and be sure to label completely. What is the name of this geometric solid?

b. Determine the amount of aluminum needed to make one can.

c. How much aluminum is needed to make 10 cans of soup.

d. If it costs $.05 cents per square inch of aluminum, how much will it cost to make 10 cans?

e. Determine the volume of one can.

f. How much soup would 10 cans of soup hold?

1.

2.

3.

Figure Volume Area

4.

10m

12m

13m

24ft

Geometry Name: ____________________________________

Unit 11 Warm-Ups Date: Wednesday, January 18th

15cm

9cm

Lateral Area:

Total Area:

25m

10m

P:

B:

h:

l:

Volume:

B:

R:

H:

L:

Volume:

Lateral Area:

Total Area:

B:

H:

r:

Volume:

Lateral Area:

Total Area:

Ds: DFGH D

Reason: _______________

None

Ds: DSTU D

Reason: ________________

None

Ds: DABC D

Reason: ________________

None

Identify CD as a Median (M), Altitude (A), Angle Bisector (AB), or Perpendicular Bisector (PB).

Decide which method(s) can be used to proof that the triangles are congruent. (SSS,ASA,SAS,AAS,HL). If there is not enough information to prove congruence, write none.

Geometry Name: ____________________________________

Unit 11 Warm-Ups Date: Thursday, January 19th

Ds: DABC D

Reason: ________________

None

Ds: DJKL D

Reason: ________________

None

Ds: DLMN D

Reason: ________________

None

7.) 8.) 9.)

10.) 11.) 12.)

1.) 15km = ________ m 2.) 406000mm = ______m 3.) 12.05km = ________mm

4.) 302.06cm = _______km 5.) 60 inches = ______ft. 6.) 6 miles = ______ yards

7.) 72 inches = ______ feet 8.) 23 miles = ______ inches

Apply the properties of parallelograms to solve for the missing sides and angles.

Geometry Name: ____________________________________

Unit 11 Warm-Ups Date: Friday, January 20th

22.) EF = ; FG =

23.) EF = ; FG =

24.) EF = ; FG =

25.) mK = ; mL = ;

mM = .

26.) mK = ; mL = ;

mM = .

27.) mK = ; mL = ;

mJ = .

28.) DE =

29.) DE =

30.) DE =

Convert all measurements in the Metric or English systems. km hm dam m dm cm mm

20.) MN = .

21.) MN = .

22.) MN = .

Geometry: Unit 11 Name: ____________________________________

Rectangular Prism Notes Date: ____________________________________

Rectangular Prism: _______________________________________________________ _____________________________________________________________________

Total Area: ____________________________________________________________ _____________________________________________________________________

Lateral Area: ___________________________________________________________

How do we find Total Area?

Example 1

Find the area of each face:

Front: ____________

Back: ____________

Top: _____________

Bottom: __________

Left Side: ________

Right Side: _______

Total: ___________

How do you find the Lateral Area? _________________________________________

Formula for the Lateral Area: _______________________________________________

Formula for the Total Area of a Rectangular Prism: _______________________________

Example 2

Find the lateral area: ________________

Find the total area: _______________

Example 3

Find the lateral area: ________________

Find the total area: _______________

6cm

8cm

10cm

6m

6m

20m

9in

9in

9in page 1


Rectangular Prism Notes Date: ____________________________________

Volume: _______________________________________________________________ _____________________________________________________________________

Formula for Volume of a Rectangular Prism: _____________________________________

Revisit Example 1: L = _____ W = ______ H = _______

Find the volume: __________





Example 4: Find the Lateral Area, Total Area, and Volume of the rectangular prism.

Lateral Area: ______________ Total Area: __________ Volume: _______________

5in

7in

13in

page 2

Geometry Name: ____________________________________

Unit 11 Class Practice Date: ____________________________________

Find the lateral area, total area, and volume of each rectangular prism on a separate sheet.

1. L = 4cm W = 3cm H = 2cm LA = ______ TA = _______ V = _______

2. L = 5m W = 3m H = 3m LA = ______ TA = _______ V = _______

3. L = 5ft W = 4ft H = 3ft LA = ______ TA = _______ V = _______

4. L = 7in W = 2in H = 4in LA = ______ TA = _______ V = _______

5. L = 3mm W = 2mm H = 6mm LA = ______ TA = _______ V = _______

H

WL

Example 1: Find the Lateral Area, Total Area and Volume of the Triangular Right Prism.

Lateral Area (L.A) = Perimeter x height

Total Area (T.A) = Lateral Area + 2(Area of the Base)

Volume (V) = Area of the Base x height of the prism

12m

12m

7m8m

12m

7m8m4m

Area of the Base:

Perimeter of the Base:

Height of Prism:

Lateral Area:

Total Area:

Volume:

14m

16m

10m 10m6m

Example 2: Find the Lateral Area, Total Area and Volume of the Triangular Right Prism.

page 3

Area of the Base:


Height of Prism:

Lateral Area:

Total Area:

Volume:

Geometry Name: ____________________________________

Other Right Prisms - Notes Date: ____________________________________

Example 3: Find the Lateral Area, Total Area and Volume of the Trapezoidal Right Prism.

8m

18m14m

30m

40

m

10m

1.

2.

100m

42m

18m

28m24m 20m

42m

24m

36m

18m12m

Page 4

Area of the Base:


Height of Prism:

Lateral Area:

Total Area:

Volume:

Practice Exercises: Find the Lateral Area, Total Area and Volume of Right Prisms.

Area of the Base:


Height of Prism:

Lateral Area:

Total Area:

Volume:

Area of the Base:


Height of Prism:

Lateral Area:

Total Area:

Volume:

Geometry Name: ____________________________________

Unit 11: Prisms Homework Date: ____________________________________

1.

2.

3.

60m

24m28m

40m16m

70m

22m

50m

24m

20m

28m

Find the Lateral Area, Total Area, and Volume of each right prism.

Page 5

4in

16in

Base is a square.

Area of the Base:


Height of Prism:

Lateral Area:

Total Area:

Volume:

Area of the Base:


Height of Prism:

Lateral Area:

Total Area:

Volume:

Area of the Base:


Height of Prism:

Lateral Area:

Total Area:

Volume:

1.

3.

6m5m

10m

12.5m7.5m

70m

50m

60

m

30m25m

Page 6

2.

50mm

25mm 28mm

Geometry Name: ____________________________________

Unit 11: Prisms Homework Date: ____________________________________

Find the Lateral Area, Total Area, and Volume of each right prism.

Area of the Base:


Height of Prism:

Lateral Area:

Total Area:

Volume:

Area of the Base:


Height of Prism:

Lateral Area:

Total Area:

Volume:

Area of the Base:


Height of Prism:

Lateral Area:

Total Area:

Volume:

Geometry Name: ____________________________________

Pyramid Notes Date: ____________________________________

Regular Pyramid - ________________________________________________________ We will be looking at square pyramids.

Lateral Area - __________________________________________________________

Total Area - __________________________________________________________

Volume - _______________________________________________________________

Therefore, we need to find the following four pieces of information for each problem:

1. Area of the base – A = e2

2. Perimeter of the base – P = 4e

3. Height – h

4. Slant height - l

Example 1 – Base Edge - _______________________________

Height – __________________________________

Slant Height – ______________________________

Area of the base – __________________________

Perimeter of the base - _______________________

Lateral Area - ______________________________

Total Area - _____________________________

Volume - _____________________________

12in = e

8in = h

Page 7

Geometry Name: ____________________________________

Pyramid Notes - Continued Date: ____________________________________


Height – __________________________________

Slant Height – ______________________________

Area of the base – __________________________


Lateral Area - ______________________________

Total Area - _____________________________

Volume - __________________________________


Height – __________________________________

Slant Height – ______________________________

Area of the base – __________________________


Lateral Area - ______________________________

Total Area - _____________________________

Volume - __________________________________

Example 4 - Base Edge - _______________________________

Height – __________________________________

Slant Height – ______________________________

Area of the base – __________________________


Lateral Area - ______________________________

Total Area - _____________________________

Volume - __________________________________

10m

12m

13m

20in

24in

16ft

17ft

Page 8

Geometry Name: ____________________________________

Unit 11 Pyramids Homework Date:

1.

2.

3.

Figure Volume Area

20.5ft

9ft

20ft

24in

14in

22m

61m

page 9

4.

18mm

9mm

12.7mm

Lateral Area:

Total Area:

P:

B:

H:

L:

Volume:

P:

B:

H:

L:

Volume:

P:

B:

H:

L:

Volume:

P:

B:

H:

L:

Volume:

Lateral Area:

Total Area:

Lateral Area:

Total Area:

Lateral Area:

Total Area:

5.

6.

7.

Figure Volume Area

Page 10

6ft3ft

4.2ft

Geometry Name: ____________________________________

Unit 11 Pyramids Homework Date:

3m

7m

2.3m

14ft

14ft

14ft

6cm

3cm3cm

1.7cm5cm

8.

P:

B:

H:

L:

Volume:

P:

B:

H:

Volume:

P:

B:

H:

Volume:

P:

B:

H:

Volume:

Lateral Area:

Total Area:

Lateral Area:

Total Area:

Lateral Area:

Total Area:

Lateral Area:

Total Area:

Geometry Name: ____________________________________

Cylinder Notes Date: ____________________________________

A cylinder is like the right prisms with which we have been working all week, except that the bases of a cylinder are circles. The volume and total area can be calculated in a very similar manner.

In a cylinder, the formula for Volume is exactly the same. Multiply the area of the base by the height. In this case the base is a circle. Recall that the area of a circle is calculated by using A = ________.

The Lateral Area and Total Area is calculated in a similar manner. However we must replace “perimeter of base” with ______________________________________, use _________

Therefore, to find the Total Area and Volume of a cylinder you must still calculate the same three pieces of information:

1. ________________ of the base – ______________

2. ________________ of the base – _____________

3. Height of the object – given

Example 1 – Find the Total Area and Volume of the given cylinder.

Radius – ____________________

Area of Base – _______________

Circumference of Base – ________

Height – ____________________

Volume –

Lateral Area –

Total Area -4in

10in

page 11

Geometry Name: ____________________________________

Cylinder Notes Date: ____________________________________

Radius – ____________________

Area of Base – _______________


Height – ____________________

Lateral Area:

Total Area:

Volume:

Radius – ____________________

Area of Base – _______________


Height – ____________________

Lateral Area:

Total Area:

Volume:

Radius – ____________________

Area of Base – _______________


Height – ____________________

Lateral Area:

Total Area:

Volume:

14m

7m

100cm

75cm

27in

22.8in

Page 12




Geometry Name: ____________________________________

Cones Notes Date: ____________________________________

Cone - ________________________________________________________________ _____________________________________________________________________

Volume - _______________________________________________________________

Lateral Area - __________________________________________________________

Total Area - __________________________________________________________

Therefore, now we need to find the four key pieces of information first:

1. Area of the base – __________________

2. Circumference of the base - _____________

3. Height - ___________

4. Slant height - ______________

Radius - ____________________________________________

Area of the base – ____________________________________

Circumference of the base – _____________________________

Height - ____________________________________________

Slant height – ________________________________________

Lateral Area - _______________________________________

Total Area - ________________________________________

Volume - ___________________________________________

10m

6m

8m

page 13

Example 1 – Find the Total Area and Volume of the given cone

Geometry Name: ____________________________________

Cones Notes - Continued Date: ____________________________________

3in

4in

15m

9m

12m

26cm

24cm

Page 14

Example 2 – Find the Total Area and Volume of the given cone.

Radius:

Area of the base:

Circumference of the base:

Height:

Slant height:

Lateral Area:

Total Area:

Volume:


Radius:

Area of the base:


Height:

Slant height:

Lateral Area:

Total Area:

Volume:

Radius:

Area of the base:


Height:

Slant height:

Lateral Area:

Total Area:

Volume:



Cylinders and Cones Homework Date: ____________________________________

1.

3.

3.

Figure Volume Area

47ft

13ft

5in

1ft

Answers should be in inches.

Lateral Area:

Total Area:

page 15

18m

18m

4.

24ft2yd

Answers should be in feet.

B:

H:

r:

Volume:

B:

H:

r:

Volume:

B:

H:

r:

Volume:

B:

H:

r:

Volume:

Lateral Area:

Total Area:

Lateral Area:

Total Area:

Lateral Area:

Total Area:


Cylinders and Cones Homework Date: ____________________________________

1.

2.

3.

Figure Volume Area

page 16

4.

8in

17in

24ft

20ft

5cm

12cm

6in

20in

20in

P:

B:

H:

Volume:

B:

H:

L:

Volume:

B:

H:

L:

Volume:

B:

H:

L:

Volume:

Lateral Area:

Total Area:

Lateral Area:

Total Area:

Lateral Area:

Total Area:

Lateral Area:

Total Area:


Sphere Notes Date: ____________________________________

Sphere - _______________________________________________________________

______________________________________________________________________

Volume - _______________________________________________________________

Total Area - __________________________________________________________

Example 1 – Find the Total Area and Volume of the Sphere

Radius - __________________________________

Volume - _________________________________

Total Area - _____________________________


Radius - __________________________________

Volume - _________________________________

Total Area - _____________________________

6in

page 17

15mm


Sphere Notes Date: ____________________________________


Radius - __________________________________

Volume - _________________________________

Total Area - _____________________________


Radius - __________________________________

Volume - _________________________________

Total Area - _____________________________

Applications: Complete the following application problems involving circles.

1.) Since ice cream is Ms. K’s favorite treat she decides to take you to Cold Stone Creamery for a tasty treat. Your server places a scoop of ice cream with a radius of 4cm on a cone with a radius of 3cm and height 15cm. It is so hot out that your ice cream begins to melt. Is the cone big enough to hold all the ice cream if it melts?

2.) A spherical fishbowl has a diameter of 24cm. To fill the fish bowl three-fourths full, about how many liters of water would you need? Give your answer to the nearest 0.1 liter. Use 3.14 for π. Note: 1000cm3 = 1 liter.

1cm

13.1ft

page 18

Geometry Unit 11 Name: ____________________________________

Spheres and Mixed Homework Date: __________________________

1.

2.

3.

Figure Volume Area

4m

8m

15m

2cm

4.3cm

page 19

10m

7m

6m

4.

B:

R:

H:

L:

Volume:

B:

H:

r:

Volume:

P:

B:

H:

Volume:

Lateral Area:

Total Area:

Lateral Area:

Total Area:

Lateral Area:

Total Area:

Geometry Unit 11 Name: ____________________________________

Spheres and Mixed Homework Date: __________________________

5.

6.

7.

Figure Volume Area

page 20

8.

14.3ft

10m

12m

13m

28ft

9m

4m

8m

P:

B:

H:

L:

Volume:

P:

B:

H:

Volume:

Lateral Area:

Total Area:

Lateral Area:

Total Area:

Geometry Name: ____________________________________

Unit 11 Review Packet Date: ____________________________________

1.

2.

3.

Calculate the volume, lateral and total area of each figure. Be sure to use the correct formulas!

61m

11ft

11ft

11ft

60m

6.1mm

14mm

CIRCLE THE SOLID

PRISM PYRAMID

CYLINDER CONE

SPHERE

h:

l:

r:

B:

Lateral Area:

Surface Area:

Volume:

p:

B:

h:

Lateral Area:

Surface Area:

Volume:

CIRCLE THE SOLID

PRISM PYRAMID

CYLINDER CONE

SPHERE

CIRCLE THE SOLID

PRISM PYRAMID

CYLINDER CONE

SPHERE

h:

r:

B:

Lateral Area:

Surface Area:

Volume:

Geometry Name: ____________________________________


5.

6.


CIRCLE THE SOLID

PRISM PYRAMID

CYLINDER CONE

SPHERE

r:

Surface Area:

Volume:

CIRCLE THE SOLID

PRISM PYRAMID

CYLINDER CONE

SPHERE

CIRCLE THE SOLID

PRISM PYRAMID

CYLINDER CONE

SPHERE

4.

3.15cm

3in

5in

h:

l:

r:

B:

Lateral Area:

Surface Area:

Volume:

18ft

12ft

h:

l:

r:

p:

B:

Lateral Area:

Surface Area:

Volume:

Geometry Name: ____________________________________


8.

9.


CIRCLE THE SOLID

PRISM PYRAMID

CYLINDER CONE

SPHERE

CIRCLE THE SOLID

PRISM PYRAMID

CYLINDER CONE

SPHERE

CIRCLE THE SOLID

PRISM PYRAMID

CYLINDER CONE

SPHERE

7.

h:

l:

r:

p:

B:

Lateral Area:

Surface Area:

Volume:

12km

12km

h:

r:

B:

Lateral Area:

Surface Area:

Volume:

5ft2ft

4ft

p:

B:

h:

Lateral Area:

Surface Area:

Volume:

25in

24in

14in

r:

Surface Area:

Volume:

Geometry Name: __________________________

Unit 11 Review Game Date: __________________________

Problem 1 –

Problem 2 –

CIRCLE THE SOLID

PRISM PYRAMID

CYLINDER CONE

SPHERE

p:

B:

h:

Lateral Area:

Surface Area:

Volume:

CIRCLE THE SOLID

PRISM PYRAMID

CYLINDER CONE

SPHERE

Problem 3 –h:

l:

r:

B:

Lateral Area:

Surface Area:

Volume:

CIRCLE THE SOLID

PRISM PYRAMID

CYLINDER CONE

SPHERE

Geometry Name: __________________________

Unit 11 Review Game Date: __________________________

Problem 4 –

Problem 5 –

CIRCLE THE SOLID

PRISM PYRAMID

CYLINDER CONE

SPHERE

h:

l:

r:

p:

B:

Lateral Area:

Surface Area:

Volume:

h:

r:

B:

Lateral Area:

Surface Area:

Volume:

CIRCLE THE SOLID

PRISM PYRAMID

CYLINDER CONE

SPHERE

Directions: Complete each word problem. Label answers. Complete on back.

1. The radius of the Earth is approximately 6380km. Assume that the Earth is a perfect sphere.

a) Calculate the surface area and volume.

b) If approximately 70% of the Earth’s surface is covered by water, how many square kilometers of water cover the planet? (HINT: Use one of the values you found in part a)

2. A solid metal sphere with a radius of 8 cm is melted down and recast as a solid cone with a radius of 8cm. Find the height of the cone.

3. A local ice cream shop has a “to-go” service for it’s customers. A small size ice cream in a square pyramid container and a large size ice cream comes in a prism shaped container.

a) What is the volume of the small container? What is the volume of the large container?

b) How many small containers do you have to buy to equal the amount of ice cream in a large container?

c) Which container gives you more ice cream for your money? Small: $2.75 Large: $6.25

distance: midpoint: x y y y 1 x 2 y § 2 1 2 1 2 x x 1. (-5

Documents