- 69 Views
- Uploaded on
- Presentation posted in: General

13-3 Volume of Spheres

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

4/3

W a i t f o r i t . . .

- Imagine that we have a disco ball.
- Now imagine that we cut one of the squares (mirrors) of the disco ball out all the way to the center, narrowing down until it comes to a point.
- We now have a pyramid.
- Just like a sphere has an infinite amount of great circles, they have an infinite amount of these pyramids.

Height=Radius of Sphere

l

- The lateral height of the pyramid cannot be the radius of the sphere because we cannot solve for an actual sphere. Instead we search for a shape that is close to a sphere (like a disco ball) and solve for that. If we try to solve for an actual sphere, we wouldn’t have a pyramid, but a curved shape, which isn’t a pyramid.
- This shape has a base that curves inward with the surface of the sphere. With a pyramid, which we CAN solve for, the lateral height would actually be longer than the radius. The height of the pyramid would be the only segment that goes from the center of the sphere to the surface of the sphere. So, we get the radius. THE END

h

l

h

- V=1/3B¹h¹+B²h²+B³h³+. . . +Bªhª
- V=1/3B¹r+B²r+B³r+. . . +Bªr
- V=1/3r(B¹+B²+B³+. . . +Bª)
- V=1/3r(4)
- V=4/3

- Volume of Infinite Pyramids
- H can be replaced with the radius
- Distributive Property
- All the bases added together would be the surface area, which is 4
- Simplify

So lets try it!Find the volume of the sphere

8cm

V= 4/3r³

4/3(8)³

4/3(512)

4/3(1608.4954)

6433.9818/3

2144.6606

V=2,144.7cm³

Your turn!!

- Find the volume of a sphere with a diameter of 22m.

22m

- V= 4/3r³
- 4/3(11)³
- 4/3(1331)
- 4/3(4181.4598)
- 16725.8393/3
- 5575.2798
- V=5575.3m³

- Find the volume of the hemisphere with a radius of 5 cm

5 cm

- 1/2(4/3)
- 1/2(4/3)
- 1/2(4/3125)
- 1/2(166.6667)
- 1/2(523.5988)
- V=261.8

- Find the volume of a hemisphere with a diameter of 8 inches.

8 in

- 1/2(4/3)
- 1/2(4/3)
- 1/2(4/364)
- 1/2(85.3333)
- 1/2(268.0825)
- V=134

- Find the volume of the hemisphere with a circumference of 37.68 m. Use 3.14 for .

C=37.68m

- 37.68
- 37.68/
- r=6
- 1/2(4/3)
- 1/2(4/3216)
- 1/2(288)
- 1/2(904.7786842)
- V=452.4

- Pre-AP pg. 704 9-22, 30, 31

Have so much fun!!!