Introduction
Unit 5: Geometric Measurement and Dimension
Lesson: Explain Derivations of Formulas of Circumference and Area of a Circle, Volume of Cylinder, Pyramid and Cone
Class: Honors Geometry
Grade: 9th/ 10th
Task
http://www.cheops-pyramide.ch/khufu-pyramid/khufu-numbers.html
1. After visiting the website above, what is the volume of Cheop's Pyramid?
2. Why were the width and lengths the same?
"Pizza" (CC BY-NC 2.0) by Mr. Ducke
http://merrellspizza.com/menu.php
3. The website gives you the diameter of the pizza. What is the radius of the pizza?
4. After identifying the radius, find the circumference of the pizza.
"Pie" (CC BY-SA 2.0) by Salim Virji
http://www.blueridgebakery.com/CakesPies
5. The website gives you the diameter of the apple pie, what is the radius?
6. After finding the radius, what is the area of the apple pie?
"leaning tower of pisa" (Public Domain) by boklm
http://www.towerofpisa.org/leaning-tower-of-pisa-facts/
7. The website gives you the diameter for the base of the Leaning Tower of Pisa, what is the radius?
8. After identifying the radius, what is the volume of the tower?
"Road Cones on Parade." (Public Domain) by Bernard Spragg
https://s-media-cache-ak0.pinimg.com/originals/b8/bf/21/b8bf21eeec0a44be65a7dbd9348c65d4.png
9. The diameter of the traffic cone is given, what is the radius?
10. Find the volume of the traffic cone.
Process
FIND A PARTNER
- Pyramid Problem: Act like the pyramid is a perfect square, even though the website has different widths for each side. Think through why the length and widths were the same.
- Pizza Problem: Find the radius of the pizza. Then use the radius to help find the circumference of the pizza.
- Apple Pie Problem: Find the radius of the apple pie. Then use the radius to help find the area of the pie.
- The Leaning Tower of Pisa Problem: Pretend the tower has the same diameter all the way up and down. Use the diameter to find the radius. Then use the radius to find the volume of the tower.
- Traffic Cone Problem: Pretend the cone has a circle base and a pointed tip. Then, find the radius and use it to find the volume of the traffic cone.
Formula Sheet:
file:///C:/Users/sas6/Downloads/Operational%20PARCC%20High%20School%20Math%20Reference%20Sheet.pdf
Evaluation
After you and your partner finish, please display your answer and problem on the board. You will go over and explain the process to the teacher and your peers. Other groups will be allowed to go up to correct another group's work.
Conclusion
HAVE A GREAT REST OF THE DAY!!!
REMEMBER...
Homework due tomorrow.
Quiz Friday on circumference, area, and volume formulas.
Extra help on classwork or homework: https://www.ixl.com/math/geometry