Geometry 7­7 Volume Spheres.notebook
Volume Spheres
• Students will use the volume formula understanding that it is the area of the base times the height.
• Students should be able to set up an equation with the given information and solve.
• Students will be given the volume and must find another dimension of the figure.
Geometry
1. Find the volume of the composite figure.
6 in
4 in
10 in
TEKs
8.6A ­ Describe the volume formula V = Bh of a cylinder in terms of its base area and its height; 8.6B ­ Model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas 8.7A ­ Solve problems involving the volume of cylinders, cones, and sphere 8.8A ­ Write one­variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants Identify the pair of angles.
x
3.
2. A cone has the same radius as a x
4.
cylinder, and exactly the same height. y
Which has a greater volume, the cone or y
the cylinder? cylinder
cone
they are the same
o
70
35o
not enough information
75o
Title Page
1.
radius r of base = 3 in.
90o
answer
1. Volume cylinder
Volume cone: 3
1/3(50
TOTAL: 502.4 + 10
2. A
Warm­Up
Practice Answers
V ≈ 94.2 in.3
2.
radius r of base = 3 in.
V ≈ 150.72 cm.3
3.
a.
Maintain Your Skills
1.
2.
C
B
b. Cone C has the greatest volume.
c. 41.9 cm3; 83.73 − 41.86 = 41.87 ≈ 41.9
d. 167.5 > 83.7 > 41.9 e. radius; doubling the height doubles the volume, but doubling the radius increases the volume by a factor of 4.
4.
5.
46.1 cm3
20 in.3
6.
732.7 = 1/3(3.14)(r2)(28)
732.7 = 29.3r2 25 = r2
5 = r
d = 2r = 2(5) = 10 in. Practice Answers
Math Humor
When √­1 asked if he could join the number line, the other square roots told him to “Get Real”.
What kind of sports have a ball?
Are there different sizes? How are these measured?
Soccer balls have different sizes. Basketballs also have different sizes. Math Fact
Latitude and longitude lines on a globe are actually circles
Turn to your neighbor and say "Volume is always Base times Height"
Introduction
Introduction
1
Geometry 7­7 Volume Spheres.notebook
Cut and tape Labsheet in your journal
3.0
Pull
Find a friend and compare the formulas for volume of a cylinder, cone and sphere.
Labsheet
Friend Transition
Be caught picking your nose constantly...
____ Volume of Spheres Date
or picking your wedgies constantly? 1. What is a sphere?
•
3­D figure, all points equal distance from center
•
two halves is hemisphere
•
edge of hemisphere is
great circle
Would You Rather
2. How to find • units cubed
the volume of • radius is half of the diameter
a sphere?
Sphere
Notes
3. What is changing dimensions?
•
how volume is affected when radius is changed
r = 3
r = 6
V = 4/3(πr3 )
(2 )
Radius doubles
Volume 8 times bigger
Notes
Notes
2
Geometry 7­7 Volume Spheres.notebook
Sam pumped up a beach ball to double its radius.
Find the volume of both balls in terms of pi.
Order these balls by volume
9 in
2 in
10 in
radius = 6 in
radius = 3 in
3 in
16 in
π33
V = in3
V = in3
V = in3
V = 288π
14.14 in3
33.49 in3
By what factor has the volume increased?
Activity
3,052.08 in3
2,143.57 in3
Least
The volume has increased by a factor of 8
4,186.67 in3
Greatest
Greatest
Activity
Closing Questions
What is the formula for volume of a sphere? (A = 4/3πr3)
What's the difference between diameter and radius? Practice
Volume of Sphere Worksheet
Practice
(2 radi = diameter) Closing Questions
3