Geometry Teachers Never Spend Time Trying to Find Materials for Your Lessons Again!
Join Our Geometry Teacher Community Today!
A hemisphere is sphere that has been cut in half. When you cut the sphere in half you are left with the great circle, plus half of a sphere. This fact can be used to find the area, and the volume of a hemisphere. The video works several example problems in which the area and volume of a hemisphere is calculated.
The last concept in this unit is hemispheres. This unit on hemispheres is building off of spheres. If you understand spheres hemispheres are really easy.
What is a hemisphere ?
You take a sphere and slice it in half.
You have the top and you have the bottom.
Like taking a orange and sharing with a sibling, you get half and they get half.
So a hemisphere is half a sphere.
To find the area of a hemisphere I need you to think for a second.
If you have half of an orange you have half of the surface area that is the skin of the orange, but don't forget that surface area also includes the flat part.
This is the face of the orange.
When you are finding the surface area of a hemisphere you not only count the curved part, you also have to count the flat part.
What is the flat part on a hemisphere, or an orange?
It is the great circle.
What is the area of the great circle? pi r squared
It is the area of a circle in relation to the sphere.
It is a round curve.
The area of a sphere is 4pi radius squared
However, we want a hemisphere so we will divide this in half.
That will be 2pi r squared.
That formula is the area of the curved part of the hemisphere.
We also have to account for the flat part of the hemisphere and that will be 2pi r squared, and we have to add one more circle to it for the flat part.
We end up with 2 pi r squared + pir squared, which gives us 3 pi r squared.
This is the formula for the surface area of a hemisphere.
including the flat part.
I wanted to show you where that came from.
Now let's look at the volume.
The volume is different.
You have an orange, slice it in half and you get half and they get half.
Is there any extra volume?
No so we will take 4/3 pi r cubed times 1/2.
We are just taking half of a sphere.
This ends up being 4/3 which is simplified to 2/3 pi radius cubed for the volume of a hemisphere.
Again the volume formula of a hemisphere is 2/3 pi radius cubed.
We get this be reducing 4/3
Let's work a forward problem.
Given a radius of 6, find the surface area and volume of a hemisphere.
The surface area will be 3 pi times the radius which is 6 squared.
6 squared is 36
so 3 times pi times 36 is 108 pi inches squared.
That is how you find surface area of a hemisphere given radius.
The volume will be similar you are just plugging in 2/3 formula.
2/3 times pi radius(6) cubed, which is 216
So 2/3 times pi times 216 and that equals 144 pi and this will be inches cubed because we are talking about volume.
Another option for the volume of a hemisphere is to take the volume of a whole sphere and divide it in half.
Math and Geometry videos to help you figure out how to solve
Math problems or review old Math concepts you may need to refresh. If you’re a Math student or teacher, we'd love to have you subscribe and join us! We upload a new video every day
Please watch: "Study Skills Teacher's Secret Guide to your Best Grades"
Tagged under: hemisphere,sphere,great circle,volume hemisphere,geometry,Area (Dimension),Volume (Dimension),moomoomath,formula surface area hemisphere,formula volume hemisphere
Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.
Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip
Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans
1. Students enter a simple code
2. You play the video
3. The students comment
4. You review and reflect
* Whiteboard required for teacher-paced activities
With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.
Carry out a quickfire formative assessment to see what the whole class is thinking
Create interactive presentations to spark creativity in class
Student teams can create and share collaborative presentations from linked devices
Turn any public video into a live chat with questions and quizzes