1. 3.4c:Surface Area and Volume of Spheres
CCSS:
GSE’s
M(G&M)–10–6 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
6.9 = r
= r

10. Solution: Using a radius of 6.9 feet, the surface area is: S = 4r2
= 4(6.9)2
=  ft.2
So, the surface area of the sphere is  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.