1. Spheres!
Section 11.4

2. 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. A hemisphere is half of a sphere. A great circle divides a sphere into two hemispheres

4. Example 1
Find the volume of the sphere. Give your answer in terms of .
Volume of a sphere.
= 2304 in3
Simplify.

5. Example 2
Find the diameter of a sphere with volume 36,000 cm3.
Volume of a sphere.
Substitute 36,000 for V.
27,000 = r3
r = 30
Take the cube root of both sides.
d = 60 cm
d = 2r

6. Example 3
Find the volume of the hemisphere.
Volume of a hemisphere
Substitute 15 for r.
= 2250 m3
Simplify.

8. Example 4
Find the surface area of a sphere with diameter 76 cm. Give your answers in terms of .
S = 4r2
Surface area of a sphere
S = 4(38)2 = 5776 cm2

9. Example 5
Find the volume of a sphere with surface area 324 in2. Give your answers in terms of .
S = 4r2
Surface area of a sphere
324 = 4r2
Substitute 324 for S.
r = 9
Solve for r.
Substitute 9 for r.
The volume of the sphere is 972 in2.

10. Example 6
Find the surface area of a sphere with a great circle that has an area of 49 mi2.
A = r2
Area of a circle
49 = r2
Substitute 49 for A.
r = 7
Solve for r.
S = 4r2
= 4(7)2 = 196 mi2
Substitute 7 for r.

11. Example 7
Find the surface area and volume of the composite figure. Give your answer in terms of .

12. Assignment:
Pg. 383 (13-15, 17-19, 24-26)