Microsoft PowerPoint - G. Topic 8 Notes_Student_Rev2/8/2018
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Use formulas routinely for finding the perimeter and area of basic prisms, pyramids, cylinders, cones, and spheres.
Vocabulary: Volume, right vs oblique
Objectives
Assignments:
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(Pg 932)18.1 #’s 2, 4, 14, 16, 21 (5 questions)
(Pg 943)18.2 #’s 1,2, 57 odd, 12, 21,22 (7 questions)
(Pg 955)18.3 #’s 24, 11, 23 (6 questions)
(Pg 967)18.4 #’s 37 odd, 12 (4 questions)
REGULAR
(Pg 943)18.2 #’s 2, 57 odd,21, 22 (5) 
(Pg 955)18.3 #’s 24 even, 11 (3) 
(Pg 967)18.4 #’s 37 odd, 12 (4)
Holt CA Course 1
Find the area of each figure described. Use 3.14 for .
1. a triangle with a base of 6 feet and a height of 3 feet
2. a circle with radius 5 in.
3.
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Volume
• The volume of a threedimensional figure is the  number of cubes it can hold. Each cube represents  a unit of measure called
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Height
Prisms and Cylinders and  its Parts
Knowing the SHAPE & area of the BASE is very important. They do not give you base on ref. sheet.
Remember!
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Sphere
If they give you the diameter, find the RADIUS by diving by 2
TIP
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AREAS of BASES
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1. (2 ft)(3.14)(5 ft)(10 ft)?
2. (5.5 in)(1/2in)(3.14)
Point? If it has a point, ALSO multiply by 1/3
3. Height Multiply by the height
2. Area  Base 
1. Identify Identify the shape
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Find the volume of each figure to the nearest tenth. A. 
Example 1A: Finding the Volume of Prisms
2. Find Area of Base
3. Multiply by Height
Does it have a point?
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Find the volume of the figure to the nearest tenth. Use 3.14 for  . B.
Example 1B: Finding the Volume of a Cylinders
2. Find Area of Base
3. Multiply by Height
4. Does it have a point?
Does it have a point?
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Find the volume of the figure to the nearest tenth. Use 3.14 for  .
7 ft
2. Find Area of Base
3. Multiply by Height
4. Does it have a point?
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Step 1 Use the Pythagorean Theorem to find the height.
Step 2 Use the radius and height to find the volume.
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Find the volume of the figure to the nearest tenth. Use 3.14 for  .
Example 1D: Finding the Volume of Pyramids
2. Find Area of Base
3. Multiply by Height
4. Does it have a point?
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A sphere is the location of points in space that are a fixed distance from a given point  called the center of a sphere. A radius of a sphere connects the center of the sphere to  any point on the sphere. A hemisphere is half of a sphere. A great circle divides a  sphere into two hemispheres
Example 1E: Finding the Volume of Pyramids
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Find the volume of the sphere. Give your answer in terms of .
Simplify.
Find the diameter of a sphere with volume 36,000 cm3.
2E. Sphere– Diameter via Volume
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3E. Sphere– Volume
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Find the volume of the figure to the nearest tenth. Use 3.14 for  . A.
10 in.
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Find the volume of the figure to the nearest tenth. Use 3.14 for  . B.
8 cm
15 cm
YOUR TURN
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Find the volume of the figure to the nearest tenth.  C.
10 ft
14 ft
12 ft
YOUR TURN
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2. Find the radius of a sphere with volume 2304 ft3.
Your Turn! Example E Find the Surface Area of the sphere.
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D = 10cm L = 15 cm
H = 13 cm R = 3.5 cm L = 9 cm
H = 60 m L = 50 m W = 40 m
D = 23 mm
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A drum company advertises a snare drum that is 4 inches high  and 12 inches in diameter. Estimate the volume of the drum.
Additional Example 2: Music Application
2. Find Area of Base
3. Multiply by Height 1. Identify Shape & Parts 
What is the Base?
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A drum company advertises a bass drum that is 12 inches high  and 28 inches in diameter. Estimate the volume of the drum.
YOUR TURN
Rectangular Prism: V = lwh or V = Bh
Triangular Prism: V = Bh Cylinder: V = r2h or
V = Bh

Vocabulary: Composite figures
HONORS
(Pg 943)18.2 #’s 8, 9, 18, 19 (4)
(Pg 955)18.3 #’s 7, 8, 12 (3)
(Pg 967)18.4 #’s 10, 13, 14* (3)
REGULAR
(Pg 943)18.2 #’s 8, 9, (2 questions)
(Pg 955)18.3 #’s 7, 8, 12 (3 questions)
(Pg 967)18.4 #’s 10, 13,  (2 questions)
Composite Figures
• A composite figure is a figure that is made up of  two or more geometric figures
It could be two  volumes _________
It could be two volumes  ____________
OR
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Volume of  barn
Volume of  rectangular 
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Example 4B: Finding Volumes of Composite Three-Dimensional Figures Find the volume of the composite figure. Round to the nearest tenth.
The volume of the rectangular prism is: 
The base area of the regular triangular  prism is: 
The volume of the regular triangular prism is: 
The total volume of the figure is the sum of the volumes.
An equilateral Triangle?  Think 306090 special 
Right triangle
3 ft
4 ft
8 ft
5 ft
Volume of  ________
Volume of  ____________ ___________
Volume of  ___________ ___________
Composite Figure a cone in a cone  or what not.  
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Example 5 Find the volume of the composite figure. Round to the nearest tenth.
The volume of the square prism is: 
Find the side length s of the base: 
The volume of the  cylinder is: 
The volume of the composite is the cylinder minus the rectangular prism. 
Vcylinder— Vsquare prism = ______________________
Vocabulary: • Cross section
HONOR 
REGULAR (Pg 986)19.1 #39 odd, 1418EVEN (6)
What is a Cross Section?
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Learn and apply the formula for the surface area of a prism,  cylinder, pyramid, cones, and spheres 
Vocabulary: Base, lateral faces, perimeter
Objectives
Assignments:
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MODULE 19: SURFACE AREA
HONORS (Pg 999)19.2 # 2, 5, 7 12, 14*, 15, 18, (7 questions) (Pg 1012)19.3 #’s 5, 89, 12, 13, 21* (6 questions) (Pg 1023)19.4 #’s 2, 3, 4, 8, 14, 15, 17* (7 questions)
REGULAR (Pg 999)19.2 # 2, 7 12, 18, (4 questions) (Pg 1012)19.3 #’s 5, 89, 12, (4 questions) (Pg 1023)19.4 #’s 3, 4, 8, 15 (4 questions)
Surface Area of Prisms & Cylinders.
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SURFACE AREA • The surface area of each of these solids is the sum  of the areas of all the faces or surfaces that enclose  the solid. For prisms and pyramids, the faces  include the solid’s bases and its lateral faces. 
• How will the answer be labeled? • Units2 because it is area!
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Steps for Finding Surface Area  1. Draw and label each face of the solid as if you had cut the solid 
apart along its edges and laid it flat. Label the dimensions. 2. Calculate the area of each face. If some faces are identical, 
you only need to find the area of one.  3. Find the total area of all the faces
Let’s start in the beginning…
Before you can do surface area or volume, you have to know the following formulas.
Circle A = π r²
Rectangle A = lw Triangle A = ½ bh
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Warm Up Find the perimeter and area of each polygon.
1. a rectangle with base 14 cm and height 9 cm
2. a right triangle with 9 cm and 12 cm legs
3. an equilateral triangle with side length 6 cm
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A. Triangular Prism – Surface Area
1. Draw and label the two  congruent bases, and the four  lateral faces unfolded into one  rectangle. Then find the areas of  all the rectangular faces.
The surface area of the prism is ______.
2. Find individual areas and add
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35 How many  triangles?
103.2
206.4
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TOP
BOTTOM
BACK
FRONT
C. Cube– Surface Area
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Find the lateral area and surface area of the right cylinder. Give your answers in terms of .
The radius is half the diameter, or 8 ft.
Top Base Bottom Base
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SURFACE AREA GENERAL • You can find the SA of any prism by using the basic  formula for SA which is 
• L + 2B= SA • L= lateral Surface area
• L= perimeter of the base x height of the prism
• B = Area of the base
SA=(Lateral Area) +2(Base Area) SA= (Base Perimeter)*height+2(Area of Base)
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1. What is the base? 
2. Find perimeter of the BASE
3. Multiply the perimeter by the height
4. Find the area of the BASE
5. Multiply area of BASE by 2
6. Add steps 3 and 5 together. 
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General SA Formula Example
The surface area of a right rectangular prism with length , width w, and height h can be written as S = 2w + 2wh + 2h.
Tip!
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The surface area formula is only true for right prisms. To find the surface area of an oblique prism, add the areas of the faces.
Caution!
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Spheres
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The diagram shows a square pyramid. The blue dashed line labeled l is the slant height of the pyramid, the distance from the vertex to the midpoint of an edge of the base.
The base of a regular pyramid is a regular polygon, and the faces are congruent isosceles triangles.
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The diagram shows a cone and its net. The blue dashed line is the slant height of the cone, the distance from the vertex to a point on the edge of the base.
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The surface area is _______ square meters.
E. Right Pyramid– Surface Area
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Find the surface area of the cone. Use 3.14 for .
The surface area is about ______ square centimeters.
F. Right Cone– Surface Area
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Find the surface area of the cone. Use 3.14 for .
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Warm Up
Find the perimeter or circumference of each figure. Use 3.14 for .
1. 2.
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Example 1: Finding Surface Areas of Composite Three-Dimensional Figures Find the surface area of the composite figure.
The surface area of the rectangular prism is
A right triangular prism is added to the rectangular prism. The surface area of the triangular prism is
Two copies of the rectangular prism base are removed. The area of the base is B = ___________.
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The surface area of the composite figure is the sum of the areas of all surfaces on the exterior of the figure.
Example 1 Continued
S = (rectangular prism surface area) + (triangular prism surface area) – 2(rectangular prism base area)
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Your Turn! Example 1 Find the surface area of the composite figure. Round to the nearest tenth.
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Example 2: Recreation Application A sporting goods company sells tents in two styles, shown below. The sides and floor of each tent are made of nylon. Which tent requires less nylon to manufacture?
Pup tent:
Tunnel tent:
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Your Turn! Example 2 A piece of ice shaped like a 5 cm by 5 cm by 1 cm rectangular prism has approximately the same volume as the pieces below. Compare the surface areas. Which will melt faster?
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Warm Up Find each measurement. 1. the radius of circle M if the diameter is 25 cm
2. the circumference of circle X if the radius is 42.5 in.
3. the area of circle T if the diameter is 26 ft
4. the circumference of circle N if the area is 625 cm2
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What is the  volume of a  sphere??
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Find the surface area of a sphere with a great circle  that has an area of 49mi2.
G. Sphere– Surface Area
Your Turn! Example G
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Explore the effects of volume and surface area by changing the scale factor
Vocabulary: Scale factor
Page 944 #11, 17 (13 questions)
REGULAR
Page 944 #11, 17 (8 questions)
• We can apply a multiplicative factor to any formula  (perimeter, circumference, volume, and surface  area)
• Way 1:
• Way 2: 
Plug in the multiplicator factor directly to the  variable from the original formula and compare the  final product to the original formula.
The effect = 
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A box measures 5 in. by 3 in. by 7 in. Explain whether tripling only the length, width, or height of the box would triple the volume of the box.
Example 1
The original box has a volume of (5)(3)(7) = 105 cm3.
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∗ ∗ 3 ∗ ∗
3 ∗ ∗ ∗
V = (5)(3)(21) =
V = (5)(9)(7) = 315 cm3
C. Tripling the width:
∗ ∗ 3 ∗ ∗
∗ ∗ 3 ∗ ∗
3 ∗ ∗ ∗
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A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling only the radius or height of the cylinder would triple the amount of volume.
Your Turn
The original cylinder has a volume of 4 • 3 = 12 cm3.
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The radius and height of the cylinder are multiplied by 
. Describe the effect on the volume.
original dimensions:
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Example 2: Sports Application
A sporting goods store sells exercise balls in two sizes, standard (22-in. diameter) and jumbo (34-in. diameter). How many times as great is the volume of a jumbo ball as the volume of a standard ball?
standard ball: jumbo ball:
A jumbo ball is about ____ times as great in volume as a standard ball. 105
The effect =  =3.7
Your Turn! Example 2
A hummingbird eyeball has a diameter of approximately 0.6 cm. How many times as  great is the volume of a human eyeball as the volume of a hummingbird eyeball?
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Apply concepts of density based on area and volume in modeling situations.
Vocabulary: Density, population density, BTU’s
Objectives
Assignments:
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HONORS
20.3 # 5, 8, 14, 1617, 20*, 22* (7 questions)
REGULAR 20.2 # 1,2,4,5,7,12, (6 questions) 20.3 # 5, 8, 14, 1617 (5 questions)
Warm up – matching formulas
What is  Density?
• Density is the amount of  matter that an object has in a  given unit of volume. 
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POPULATION  DENISTY
• Population Density is the  population per unit area of a  specific region. In other  words, how many people (or  creatures) live per square  unit.
• Population Density = 
MEASURES OF ENERGY
• BTU means British Thermal Units, a  unit of energy, which is used to  measure the amount of energy  necessary to heat up 1 pound of water  by 1° F. 
• Measures of Energy = 
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Density Warm Up 1. If a metal has a mass of 154 g and has a volume of 14 cm3, what is its 
density?  
2. If butter has a mass of 220, what is the density of  250 mL of butter?  
3. If water has a density of 0.997 g/mL what volume must 43.2 g of  water have?  
4. HONORS: A block of oak (wood) has a density of 0.774 g/cm3, mass of  113 g, length of 84.5 mm, and width of 71.0 mm.  What is the  thickness of this block of wood?   (Hint:  you may want to take 2 steps)
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A swimming pool is a rectangular prism. Estimate the volume of water in the pool in  gallons when it is completely full (Hint: 1 gallon ≈ 0.134 ft3). The density of water is  about 8.33 pounds per gallon. Estimate the weight of the water in pounds.
Additional Example 1: Recreational Application
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Step 1 Find the volume of the swimming pool in cubic feet. 
Step 2 Use the conversion factor  . .
to estimate the volume in gallons.
Example 3 Continued
Step 3 Use Density =  to solve for mass
The swimming pool holds about _______ gallons. The water in the swimming pool weighs about _________ pounds.
A swimming pool is a rectangular prism. Estimate the volume of water in the pool in  gallons when it is completely full (Hint: 1 gallon ≈ 0.134 ft3). The density of water is about  8.33 pounds per gallon. Estimate the weight of the water in pounds.
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Additional Example 2: Recreational Application
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Example 2
What if…? Estimate the volume in gallons and the weight of the water in the aquarium  if the height were doubled.
Step 1 Find the volume of the aquarium in cubic feet.
V = wh =
the volume in gallons.
Example 2 - CONTINUED
What if…? Estimate the volume in gallons and the weight of the water in the aquarium  if the height were doubled.
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estimate the weight of the water.
The swimming pool holds about _______ gallons. The water in the swimming pool weighs about _________ pounds.
Example 2B: Finding Lateral Areas and Surface Areas of Right Cylinders Find the lateral area and surface area of a right cylinder with circumference 24 cm and a height equal to half the radius. Give your answers in terms of .
Step 1 Use the circumference to find the radius.
Step 2 Use the radius to find the lateral area and surface area. The height is half the radius, or 6 cm.
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Your Turn! Example 2 Find the lateral area and surface area of a cylinder with a base area of 49 and a height that is 2 times the radius.
Step 1 Use the circumference to find the radius.
Step 2 Use the radius to find the lateral area and surface area. The height is twice the radius, or 14 cm.
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What is a  constraint?
Constraints give you a value to be  substituted into an equation relating a  dimension to a volume or surface area,  allowing the equation to be solved, and  the dimensions found. 
Starting 20.3
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