Geometry Spheres

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Geometry Spheres
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Warm Up

• Describe the effect on the volume that results
  from the given change.
• The side length of a cube are multiplied by ¾.
• The height and the base area of a prism are
  multiplied by 5.

1) the volume is decreased by 27/64 times. 2) the
volume is increased by 25 times.
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Spheres
A sphere is the locus 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 to any point on the sphere. A hemisphere
is half of a sphere. A great circle divides a
sphere into two hemispheres.
Radius
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The figure shows a hemisphere and a cylinder with
a cone removed from its interior. The cross
sections have the same area at every level, so
the volumes are equal by Cavalieris Principle.
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Volume of a Sphere
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Finding Volumes of Spheres
A) The volume of the sphere
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C) The volume of the hemisphere
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Now you try!
1) 11.7 ft
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Biology Application
Giant squid need large eyes to see their prey in
low light. The eyeball of a giant squid is
approximate a sphere with a diameter of 25 cm,
which is bigger than a soccer ball. A human
eyeball is approximate a sphere with a diameter
of 2.5 cm. How many times as great is the volume
of a giant squid eyeball as the volume of a human
eyeball?
A giant squid eyeball is about 1000 times as
great in volume as a human eyeball.
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Now you try!
2) A hummingbird eyeball has a diameter of
approximately 0.625 cm. How many times as great
is the volume of a human eyeball as the volume of
a hummingbird eyeball. A human eyeball is
approximate a sphere with a diameter of 2.5 cm. ?
2) the volume of human eye ball is 64 times the
volume of humming bird.
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In the figure, the vertex of the pyramid is at
the center of the sphere. The height of the
pyramid is approximate the radius r of the
sphere. Suppose the entire sphere is filled with
n pyramids that each have base area B and height
r.
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Surface Area of a Sphere
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Finding Surface Area of Spheres
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Now you try!
3) Find the surface area of the sphere.
3) 2500? cm2
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Exploring Effects of Changing Dimensions
The radius of the sphere is tripled. Describe the
effect on the volume.
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Now you try!
4) The radius of the sphere above is divided by
3. Describe the effect on the surface area.
4) the volume decrease by 9 times.
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Finding Surface Areas and Volumes of Composite
Figures
Step 1 Find the surface area of the composite
figure. The surface area of the composite figure
is the sum of the surface area of the hemisphere
and the lateral area of the cone.
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Step 2 Find the volume of the composite figure.
First find the height of the cone.
The volume of the composite figure is the sum of
the volume of the hemisphere and the volume of
the cone.
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Now you try!
5) Find the surface area and volume of the
composite figure.
5) 57? ft2
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Now some problems for you to practice !
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Assessment

• The volume of the
• hemisphere

B) The volume of the sphere
1a) 887.33 ? in3 1b) 1.33 ? m3.
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2)Approximately how many times as great is the
volume of the grapefruit as the volume of the
lime?
2) 8 times
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• The surface area of
• the sphere

B) The surface area of the sphere
3a) 256? yd2 3b) 196? cm2.
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4) Describe the effect of each change on the
given measurement of the figure.

• Surface area
• The dimensions are doubled.

B) Volume The dimensions are multiplied
by ¼.
4a) Increases by 4 times 4b) Decreases by 64
times.
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5) Find the surface area and volume of the
composite figure.
5a) SA 36? ft3 V 30.67? ft3
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Lets review
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Spheres
A sphere is the locus 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 to any point on the sphere. A hemisphere
is half of a sphere. A great circle divides a
sphere into two hemispheres.
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The figure shows a hemisphere and a cylinder with
a cone removed from its interior. The cross
sections have the same area at every level, so
the volumes are equal by Cavalieris Principle.
Next Page
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(No Transcript)
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Volume of a Sphere
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Finding Volumes of Spheres
A) The volume of the sphere
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C) The volume of the hemisphere
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Biology Application
Giant squid need large eyes to see their prey in
low light. The eyeball of a giant squid is
approximate a sphere with a diameter of 25 cm,
which is bigger than a soccer ball. A human
eyeball is approximate a sphere with a diameter
of 2.5 cm. How many times as great is the volume
of a giant squid eyeball as the volume of a human
eyeball?
A giant squid eyeball is about 1000 times as
great in volume as a human eyeball.
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In the figure, the vertex of the pyramid is at
the center of the sphere. The height of the
pyramid is approximate the radius r of the
sphere. Suppose the entire sphere is filled with
n pyramids that each have base area B and height
r.
Next Page
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(No Transcript)
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Surface Area of a Sphere
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Finding Surface Area of Spheres
Next Page
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(No Transcript)
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Exploring Effects of Changing Dimensions
The radius of the sphere is tripled. Describe the
effect on the volume.
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Finding Surface Areas and Volumes of Composite
Figures
Step 1 Find the surface area of the composite
figure. The surface area of the composite figure
is the sum of the surface area of the hemisphere
and the lateral area of the cone.
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Step 2 Find the volume of the composite figure.
First find the height of the cone.
The volume of the composite figure is the sum of
the volume of the hemisphere and the volume of
the cone.
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You did a great job today!