12.6 – Surface Area and Volume of Spheres

LAST NOTES OF THE YEAR!

SPHERE NOT!

Sphere: The set of all points in space equidistant from a given point

Radius: Length from the center of the sphere to all the sides of the sphere

Hemisphere: Half a sphere

Great Circle: Plane that contains the center of the sphere, the radius is the same as the one for the sphere

Surface Area of a Sphere:

Surface Area of a Sphere:

24SA rπ=

Volume of a Sphere:

343

V rπ=

Find the surface area.24SA rπ=

24 (6)SA π=

2144SA cmπ= SA =4π(36)

Find the surface area.24SA rπ=

24 (11)SA π=

2484SA inπ=11 11 SA =4π(121)

Find the volume.34

3V rπ=

34 (5)3

V π=

V ≈166.67πm 3

4 (125)3

V π=

Find the volume.34

3V rπ=

34 (10.5)3

V π=

31543.5V ydπ=

4 (1157.625)3

V π=

10.5 10.5

The center of the sphere is C and its circumference is 17π feet.

a. What is half of the sphere called?

Hemisphere

The center of the sphere is C and its circumference is 17π feet.

b. Find the radius of the sphere.

2C rπ=17 2 rπ π=

8.5 ft r=

2π 2π

The center of the sphere is C and its circumference is 17π feet.

c. Find the diameter of the sphere.

r = 8.5ft

d = 17ft

The center of the sphere is C and its circumference is 17π feet.

d. Find the volume of the hemisphere.

343

V rπ=

€

V = 43

π (8.5)3

€

V = 43

π (614.125)

V ≈818.83π ft3

V ≈409.42π ft3

€

12

SA = 324π ft2

Find the radius of a sphere with the given information.

24SA rπ=2324 4 rπ π=

281 r=

9 ft r=

4π 4π

Find the radius of a sphere with the given information.

V = 36π in3

343

V rπ=

34363

rπ π=34

34

327 rπ π= 327 r=3in r=

π π

Find the radius of a sphere with the given information.

V = 2304π yd3

343

V rπ=

3423043

rπ π=34

34

31728 rπ π=31728 r=

12yd r=