Download Geometry H

Geometry & Finite H
Mr. Russo
Name: _______________________
Date: _______________________
SA & V of Spheres
Definition of a sphere:
The distance from the center to the sphere is called the __________.
A segment passing thru the center connecting 2 points on the sphere is a __________.
If a plane intersects a sphere, the intersection is a __________.
If the circle’s center is the center of the sphere, that circle is a great circle.
There are various ways to think about the formula for the surface area of the sphere. Deriving the formula
requires calculus, which we’re not ready for yet. But here is 1 way we can think about it:
These 2 pieces could be put together to make a sphere. Each piece is about 2
circles, for a total of 4 circles. So, it makes sense that the surface area of a
sphere is: SAsphere =
We can use the SA of a sphere to figure out the formula for the volume of a sphere.
So, adding up the volumes of all “n” pyramids would be…
Vsphere =
For #1-2, find the SURFACE AREA and VOLUME of each sphere, and give exact answers (in terms of ).
For #3, find the SURFACE AREA and VOLUME of the sphere, and round to the nearest hundredth.
3.) A sphere in which the area of a great circle = 48.7 m2.
Find the SA and V of each composite figure. Give exact answers, and round to the nearest hundredth if needed.
4.) Cylinder with hemisphere on top
5.) Prism with hemisphere removed
6.) Cone with hemisphere on top
Answers!
1372
16384
in.³
2.) SA = 1024 m², V =
m³
3
3
3.) r  3.937 m, so SA = 194.80 m², V = 255.66 m³
368
4.) SA = 88 in.²  276.46 in.², V =
 in.³  385.37 in.³
3
5.) SA = 720 + 25 cm²  798.54 cm²,
6.) SA = 98  7 170 cm²  594.61 cm²,
250
1225
V = 1300 –
 cm³  1038.20 cm³
V=
 cm³  1282.82 cm³
3
3
1.) SA = 196 in.², V =