I’m studying and need help with a Mathematics question to help me learn.
THIS DISCUSSION HAS 3 PARTS:
Discussion Post_July 2:
Activity 1: Surface Area Formulas
- Choose one cylinder and it’s corresponding cone (same base and height)
- Use the Nets to come up with a formula for the surface area of these two 3D shapes. (FYI: the “net” of a 3D shape is when it is opened and unfolded to create a flat shape. The flat shape is called a “net”. The “net” is what I provided for you on June 27)
- Can you generalize these formulas for any cylinder? And any cone?
For the discussion post, write your derived formula for the surface area of a cylinder and a cone. How did you find this?
Activity 2: Surface Area Video
- Watch the video titled “Surface Area of Cylinders.”
- In this video, students are discussing the surface area of a cylinder.
For the discussion post, answer the following questions:
- What teacher moves helped the students in the video generate the formula for the surface area of a circle-based cylinder?
- How would you want to respond to the student’s last question in the video?
Activity 3: Surface Area of a Sphere (“Orange” You Glad?)
You are going to use an orange to investigate the surface area of a sphere.Before you begin, make sure you know the definition of surface area, radius, and circumference.
- Paper plate
- Squeeze and roll one orange around making it as spherical as possible.
- Cut the orange into two equal halves (hemispheres) to reveal a great circle of the orange.
- Lay the orange face down on a paper plate and trace it.
- PREDICT how many great circles can be covered with the pieces of your orange peel.___________
- Trace several more great circles onto the plate.
- Tear off pieces of the orange peel, each about 1 square inch (or slightly smaller) in size.
- Place pieces in one of the circles. Fill the circle as much as possible without overlapping the pieces.
- Continue filling circles until you are out of orange peel.
Use your results to answer the following questions in complete sentences.
- Write a (general) mathematical expression that tells the amount of area you covered on a single circle.Be sure to define your variables.______________________________
- How many circles did you cover in all? ______ Based on this result, write a mathematical expression that tells the surface area of your orange (sphere). _________________
For the discussion post, write your derived formula for the surface area of a sphere. How did you find this?