Write down this problem on your
READY RECALL SHEET
Be prepared to explain your answer
if you are called on.
KNOW these formulas:
= πr2
area of a circle
volume of a cylinder
= πr2h
volume of a cone
= πr2h
3
find the volume of a
hemisphere with a radius
Page xx
of
14
meters.
of your INB
“CNN” reports
66 feet wide
100 feet deep
ITEMS of BUSINESS
Test coming up on Feb. 23/24
Have your homework
out on your desk.
Try this CHALLENGE question:
Cone is 1/3 the volume of
the cylinder. The area left
would be 2/3 of the
cylinder’s volume.
V=
2
π𝑟 2 h
3
=
2
π32 5
3
= 94.2477… = 94.2 𝑖𝑛3
LINE AND ANGLE RELATIONSHIPS
10.5 Volume of a Sphere
Get into your Groups
We will be using the
foldable we made
last time.
find the
volume of a hemisphere
with a radius of
14 meters.
Page xx
of your INB
W
SPHERES
hy don’t we ever see planets shaped like cylinders or cones? Everywhere
we look in space, planets—and even stars like our sun—are shaped like spheres.
Why is that?
The answer is gravity. For a large body in space, gravity pulls every point on the surface equally toward
its center. Over time, gravity molds the body into the only possible shape that could form from such a
process—a sphere!
Of course, not every object we observe in space is a sphere. Asteroids, comets, and even very small
moons often have weird, rough shapes. These objects are too small—and their gravities too weak. For
them, the sphere-making process never begins.
SPHERES
Circumference
radius
diameter
Distance around the
widest part of a sphere.
C = πd
or C = π2r
LETS TRY SOME PROBLEMS
List the radius, diameter, and circumference for each problem. Use the π key on
the calculator and round to the tenths place.
Radius:
Radius:
Radius:
Diameter:
Diameter:
Diameter:
Circumference:
C = πd
C = π2r
Circumference:
C = πd
C = π2r
Circumference:
C = πd
C = π2r
FINDING THE
VOLUME OF A SPHERE
ACTIVITY
Let’s place a sphere in a cylinder with the same radius and height. How
much of the cylinder do you think the sphere uses?
h = 8m
V (cylinder) = π𝑟 2 h ≈ 402.1 𝑚3
r=4m
SOOOO…. If the Volume of a Cylinder is
about 402.1 𝑚3 , what is your guess for the
Volume of the Sphere with the
same radius and height?
(write it down and show your partner).
Volume of a Sphere Demonstration Video
https://www.youtube.com/watch?v=8jygxFuLoCk
The volume of the sphere is
2
3
of 402.1 ≈ 268.1 𝑚3
DERIVING THE VOLUME OF THE SPHERE
height
Volume of a Sphere
2
= (Volume of a Cylinder)
3
2
= (π𝑟 2 ℎ)
3
2
= [π𝑟 2 (ℎ𝑒𝑖𝑔ℎ𝑡 = 𝑑𝑖𝑎𝑚𝑡𝑒𝑟 = 2𝑟)]
3
=
2
(π𝑟 2 2𝑟)
3
=
4
π𝑟 3
3
INB NOTEBOOK ACTIVITY
Write the
parts of
the figure.
V=
r
V=
4
π𝑟 3
3
4
π63
3
= 904.7786…
≈ 904.8 𝑖𝑛3
Write the formula and
find the volume of the
example shown.
V=
V=
2
π𝑟 2 ℎ
3
4
π𝑟 3
3
LETS TRY SOME PROBLEMS
Calculate the volume for each sphere. Use the π key on the calculator.
Round decimals to the nearest tenth. Write out each formula.
HEMISPHERE
Talk in your groups…
Remind each other what a hemisphere is.
Discuss how the volume of a sphere is different than the volume of a hemisphere?
V(hemisphere) = V =
4
π𝑟 3
3
2
or =
2
π𝑟 3
3
CHAPTER 10 VOCAB ORGANIZER
CHAPTER 10 VOCAB ORGANIZER
Let’s Review what we found.
V=
4
π𝑟 3
3
V=
2
π𝑟 3
2
r
10.5 Volume of a Sphere
Day 1 – Integer operations,
PEMDAS, evaluating
find the volume of
a hemisphere with a radius
of 14 meters.
Number 14 on your Homework
LETS TRY SOME PROBLEMS
Worksheet
10.5
Volume
of a
Sphere
