Mr. Saputo's Geometry Class
5/7/2015
11.6 Spheres
Learning Objective: Surface area and volume of a
sphere.
Spheres
• A sphere is the locus of points in space that are a
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Spheres
given distance from a point called the center of the
sphere.
A radius of a sphere is a segment from the center
to a point on the sphere.
A chord of a sphere is a segment whose endpoints
are on the sphere.
A diameter of a sphere is a chord that contains the
center.
If a plane that intersects a sphere contains the center
of the sphere, the intersection is a great circle of
the sphere.
A great circle of a sphere separates the sphere into
two congruent halves called hemispheres.
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Mr. Saputo's Geometry Class
5/7/2015
Go to the app
Surface Area
• Surface Area of a Sphere The
surface area S of a sphere with
radius r,
𝑆 = 4𝜋𝑟 2.
Find the surface area of the
sphere to the right.
Spheres
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Mr. Saputo's Geometry Class
5/7/2015
Find the surface area of the sphere.
Using a Great Circle
• The circumference of a great circle of a
sphere is 25 inches. Find the surface area
of the sphere.
• NOTE: Begin by finding the radius of
the sphere. Then using a radius of ____
cm, find the surface area.
Spheres
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Mr. Saputo's Geometry Class
5/7/2015
Try one
• Find the surface area of the sphere.
Finding the Volume of a Sphere
• Volume of a Sphere The
volume V of a sphere with
radius r is,
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𝑉 = 3 𝜋𝑟 3 .
Find the volume of the sphere to
the right. Because there is a
decimal, we will find the volume
with decimals.
Spheres
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Mr. Saputo's Geometry Class
5/7/2015
You try it!
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2.
• Find the Volume
• Find the Volume
Problem
• What is the radius of a sphere made from the cylinder of
modeling clay shown? Assume the sphere has the same
volume as the cylinder.
• HINT: To find the volume of the cylinder of modeling clay,
use the formula for the volume of a cylinder. Then use that
volume to find the radius. You will need a calculator.
Spheres
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Mr. Saputo's Geometry Class
5/7/2015
Cross-sections
• Find the area of the
intersection of the sphere and
plane. Leave your answers in
terms of 𝜋.
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2.
Composite Problems
• Storage Tank A grain storage tank shown
at the right is in the shape of a cylinder
covered by a half sphere. If the height of
the cylinder is 50 feet and it is 80 feet in
diameter, find the total surface area
(including the base) and volume of the
tank.
Spheres
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Mr. Saputo's Geometry Class
5/7/2015
Homework = WKST
Spheres
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