Lesson 3A: Conics (Bartels M3H)

Last updated 10 months ago

5 questions

Instructions

3A: I can find arc length & area of a sector of a circle using proportional reasoning

HI CLASS

Since you have a sub today - here are self guided notes. Please turn to the first page in your new packet and follow along! 

Any questions can be answered tomorrow. This is content that was learned last year, so see how well you can remember it!

Example 1: Given circle P with a radius of 8 and m\angle{APC}=120\degree, find the length of arc AC.

Since we are finding arc length - use circumference 2\pi{r}

What is the length of arc AC?_______ 
Keep your answer in terms of \pi or round to 2 decimal places.

Example 2: Given circle P with a circumference of 10\pi and m\angle{APC} = 100 \degree, find the area of the shaded region.
 
FIRST: Find the radius 
r=_______ 

Since we are finding area of a sector - use area formula \pi{r^2}

What is the area of the shaded region?_______ 
Keep your answer in terms of \pi or round to 2 decimal places.

Example 3: Given circle P and m\angle{APB} = 60 \degree, find the area of the shaded region.


1. First find the area of the sector using r=6 and degree=60\degree . What did you get?_______ 

2. Find the area of the area of the triangle: {bh}/2
What did you get?_______ 
click to see the first hint if you are having trouble with this. 

3. Subtract the area of the sector and the triangle to find the shades region. 
What did you get?_______
Keep your answer in terms of \pi or round to 2 decimal places.

YOU TRY: Find the area of the shaded region.

1. Sector area:_______ 
2. Area of riangle:_______ 
3. Shaded Region:_______

Keep your answer in terms of \pi or round to 2 decimal places.

Example 4: A piece of gum is stuck to the bottom of a tire on Mila’s scooter. In order to get it off, she must rotate the tire 74°. When Mila does this, how far does the piece of gum travel? Note that the tire has a radius of 6 inches.

Arc Length:_______ 

Keep your answer in terms of \pi or round to 2 decimal places.

Do not worry about the last 3 questions. 

For the rest of class work on the 3.1 Pizza Task (all 3 pages) in your packet. I will be collecting this for a grade at the end of class on TUESDAY