KNOW these formulas: area of a circle volume of a cylinder volume of a cone

i-can

Page xx of your INB

Write down this problem on your

READY RECALL SHEETBe prepared to explain your answer

if you are called on.

find the volume of a hemisphere with a radius of 14 meters.

= πr2

= πr2h

= πr2h 3

“CNN” reports66 feet wide

100 feet deep

ITEMS of BUSINESS

Test coming up on Feb. 23/24

Have your homework out on your desk.

RE- 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 = πh = π5 = 94.2477… = 94.2

LINE AND ANGLE RELATIONSHIPS

10.5 Volume of a Sphere

Page xx of your INB

i-can

Get into your Groups

We will be using the foldable we made

last time.

find the volume of a hemispherewith a radius of 14 meters.

SPHERES

Why don’t we ever see planets shaped like cylinders or cones?

Everywherewe look in space, planets—and even stars like our sun—are shaped like spheres.Why is that?

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.

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!

SPHERES

Circumference

radiusdiameter

Distance around the widest part of a sphere.

C = πdor 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:

Diameter:

Circumference:

Radius:

Diameter:

Circumference:

Radius:

Diameter:

Circumference:C = πdC = π2r

C = πdC = π2r

C = πdC = π2r

h =

8m

FINDING THE VOLUME OF A

SPHERE

ACTIVITYLet’s place a sphere in a cylinder with the same radius and height.

How much of the cylinder do you think the sphere uses?

V (cylinder) = πh 4

r=4mSOOOO…. If the Volume of a Cylinder is

about 4, 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 Videohttps://www.youtube.com/watch?v=8jygxFuLoCk

The volume of the sphere is of 402.1 268.1

DERIVING THE VOLUME OF THE SPHEREh

eig

ht radius

Volume of a Sphere = (Volume of a Cylinder)

= π

= π

= π

= π

INB NOTEBOOK ACTIVITY

Write the parts of

the figure.

Write the formula and find the volume of the

example shown.

V = π

V = π

= 904.7786… 904.8

r V = π

V = π

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?

2

V(hemisphere) = V = π

or = π

CHAPTER 10 VOCAB ORGANIZER

CHAPTER 10 VOCAB ORGANIZER

Let’s Review what we found.

V = π r

V = π

Day 1 – Integer operations, PEMDAS, evaluating10.5 Volume of a Sphere

i-can find the volume ofa hemisphere with a radiusof 14 meters.

Number 14 on your Homework

LETS TRY SOME PROBLEMS

Worksheet10.5

Volume of a

Sphere