Distance: Midpoint: x y y y 1 x 2 y § 2 1 2 1 2 x x 1. (-5 ...
Transcript of 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
Geometry: Unit 11 Name: ____________________________________
Rectangular Prism Notes Date: ____________________________________
Volume: _______________________________________________________________ _____________________________________________________________________
Formula for Volume of a Rectangular Prism: _____________________________________
Revisit Example 1: L = _____ W = ______ H = _______
Find the volume: __________
Revisit Example 2: L = _____ W = ______ H = _______
Find the volume: __________
Revisit Example 3: 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:
Perimeter 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:
Perimeter 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:
Perimeter of the Base:
Height of Prism:
Lateral Area:
Total Area:
Volume:
Area of the Base:
Perimeter 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:
Perimeter of the Base:
Height of Prism:
Lateral Area:
Total Area:
Volume:
Area of the Base:
Perimeter of the Base:
Height of Prism:
Lateral Area:
Total Area:
Volume:
Area of the Base:
Perimeter 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:
Perimeter of the Base:
Height of Prism:
Lateral Area:
Total Area:
Volume:
Area of the Base:
Perimeter of the Base:
Height of Prism:
Lateral Area:
Total Area:
Volume:
Area of the Base:
Perimeter 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: ____________________________________
Example 2 – Base Edge - _______________________________
Height – __________________________________
Slant Height – ______________________________
Area of the base – __________________________
Perimeter of the base - _______________________
Lateral Area - ______________________________
Total Area - _____________________________
Volume - __________________________________
Example 3 – Base Edge - _______________________________
Height – __________________________________
Slant Height – ______________________________
Area of the base – __________________________
Perimeter of the base - _______________________
Lateral Area - ______________________________
Total Area - _____________________________
Volume - __________________________________
Example 4 - Base Edge - _______________________________
Height – __________________________________
Slant Height – ______________________________
Area of the base – __________________________
Perimeter 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 – _______________
Circumference of Base – ________
Height – ____________________
Lateral Area:
Total Area:
Volume:
Radius – ____________________
Area of Base – _______________
Circumference of Base – ________
Height – ____________________
Lateral Area:
Total Area:
Volume:
Radius – ____________________
Area of Base – _______________
Circumference of Base – ________
Height – ____________________
Lateral Area:
Total Area:
Volume:
14m
7m
100cm
75cm
27in
22.8in
Page 12
Example 2 – Find the Total Area and Volume of the given cylinder.
Example 3 – Find the Total Area and Volume of the given cylinder.
Example 4 – Find the Total Area and Volume of the given cylinder.
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:
Example 3 – 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:
Circumference of the base:
Height:
Slant height:
Lateral Area:
Total Area:
Volume:
Example 4 – Find the Total Area and Volume of the given cone.
Geometry: Unit 11 Name: ____________________________________
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:
Geometry: Unit 11 Name: ____________________________________
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:
Geometry: Unit 11 Name: ____________________________________
Sphere Notes Date: ____________________________________
Sphere - _______________________________________________________________
______________________________________________________________________
Volume - _______________________________________________________________
Total Area - __________________________________________________________
Example 1 – Find the Total Area and Volume of the Sphere
Radius - __________________________________
Volume - _________________________________
Total Area - _____________________________
Example 2 – Find the Total Area and Volume of the Sphere
Radius - __________________________________
Volume - _________________________________
Total Area - _____________________________
6in
page 17
15mm
Geometry: Unit 11 Name: ____________________________________
Sphere Notes Date: ____________________________________
Example 3 – Find the Total Area and Volume of the Sphere
Radius - __________________________________
Volume - _________________________________
Total Area - _____________________________
Example 4 – Find the Total Area and Volume of the Sphere
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: ____________________________________
Unit 11 Review Packet Date: ____________________________________
5.
6.
Calculate the volume, lateral and total area of each figure. Be sure to use the correct formulas!
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: ____________________________________
Unit 11 Review Packet Date: ____________________________________
8.
9.
Calculate the volume, lateral and total area of each figure. Be sure to use the correct formulas!
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