3.4c:Surface Area and Volume of Spheres

1
3.4cSurface 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
2
Finding 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?
3
Finding the Surface Area of a Sphere

• A chord of a sphere is a segment whose endpoints
  are on the sphere.

4
Surface Area of a Sphere

• The surface area of a sphere with radius r is S
  4?r2.

5
Finding the Surface Area of a Sphere

• Find the surface area. When the radius doubles,
  does the surface area double?

6

• S 4?r2
• 4?22
• 16? in.2

• S 4?r2
• 4?42
• 64? in.2

The 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.
7
More . . .

• 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.

8
Ex. 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?

9
Solution

• Begin by finding the radius of the sphere.
• C 2?r
• 13.8? 2?r
• 13.8?
• 2?r
• 6.9 r

r
10
Solution

• 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
11
Theorem Volume of a Sphere

• The volume of a sphere with radius r is V

3
12
Find the Volume of a sphere with a radius of 5
in.
13
Find the total surface area and Volume
14
The 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.
15
(No Transcript)