warm up give the formulas for the volume of the following figures...
TRANSCRIPT
Warm Up
Give the formulas for the volume of the following figures
Cylinder:__________________Prism:__________________
Pyramid:__________________Cone:___________________
What is a Sphere?
• A sphere is a set of all point in space equidistant from a given point called the center.
• This sounds just like the definition of a circle.
• What differences do you notice about the sphere(to the left) and a regular circle?
r
Radius of a Sphere
Just like a circle a Sphere
has a radius and a diameter
as well!!!!
So what can we say about the diameter?
A radius is a segment that
has one endpoint at the center and the other endpoint on the sphere.
If you cut a sphere right down the middle you would create two congruent halves called HEMISPHERES.
You can think of the globe. The equator cuts the earth into the northern and southern
hemisphere.Which
hemisphere do we live on?
Look at the cross section formed when you cut a sphere in half.
What shape is it?
A circle!!! This is called the GREAT CIRCLE of the sphere.
This is where the diameter and the radius are located.
Unlike circles the diameter and radius have to go through a particular part of the sphere.
5 in
Volume of a SphereA spherical balloon has an initial radius of 5 in. When more air is added, the radius becomes 10 in. Explain how the volume changes as the radius changes.
2 2523.6 in . 4,118.8 inV vs
10 in
34
3V r
? cm
Find the diameterV
r
( )4
3
3
3(500 ) (4 r )
3 3
3(500 ) cm
3V
3(4 r )500
3500r
4
3125 r5 r 10 d
What about finding the volume of a hemisphere?
Formula: A hemisphere is
half of a sphere so just take half of the formula for volume
of a sphere.