Title: 3.4c:Surface Area and Volume of Spheres
13.4cSurface Area and Volume of Spheres
CCSS
GSEs
M(GM)106 Solves problems involving perimeter,
circumference, or area of two dimensional figures
(including composite figures) or surface area or
volume of three
2Finding the Surface Area of a Sphere
- Sphere- all of the points in space that are the
same distance from a point.
How is this different from a circle?
3Finding the Surface Area of a Sphere
- A chord of a sphere is a segment whose endpoints
are on the sphere.
4Surface Area of a Sphere
- The surface area of a sphere with radius r is S
4?r2.
5Finding the Surface Area of a Sphere
- Find the surface area. When the radius doubles,
does the surface area double?
6The surface area of the sphere in part (b) is
four times greater than the surface area of the
sphere in part (a) because 16? 4 64? ?So,
when the radius of a sphere doubles, the surface
area DOES NOT double.
7More . . .
- If a plane intersects a sphere, the intersection
is either a single point or a circle. If the
plane contains the center of the sphere, then the
intersection is a great circle of the sphere.
Every great circle of a sphere separates a sphere
into two congruent halves called hemispheres.
8Ex. 2 Using a Great Circle
- The circumference of a great circle of a sphere
is 13.8? feet. What is the surface area of the
sphere?
9Solution
- Begin by finding the radius of the sphere.
- C 2?r
- 13.8? 2?r
- 13.8?
- 2?r
- 6.9 r
r
10Solution
- Using a radius of 6.9 feet, the surface area is
- S 4?r2
- 4?(6.9)2
- 190.44? ft.2
So, the surface area of the sphere is 190.44 ?
ft.2
11Theorem Volume of a Sphere
- The volume of a sphere with radius r is V
3
12Find the Volume of a sphere with a radius of 5
in.
13Find the total surface area and Volume
14The circumference of the cone is 3 inches
The cone is completely packed with Ice cream,
and there is exactly half a scoop on top.
Find how much ice cream you will receive.
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