Download Teacher Notes - KEY CRS PPF 703 – Use relationships among

CW#35: Find Arc LENGTH
Geometry
Teacher Notes - KEY
CRS
Objective
PPF 703 – Use relationships among circles, arcs, and distances in circles
13.3 Find length of arcs
Yesterday, we found arc MEASURE:
2) Solve for x. Assume that lines which appear to be diameters are actual diameters.
Today, we will find the LENGTH of an arc.
Quick Review:
Review Example:
STAY READY.
Have students try #1-3 in CW
*Write into notes*
Finding Arc Length:
Step 1: Use radius or diameter to find circumference.
Step 2: Divide central angle measure by 360
Step 3: Multiply step 1 (circumference) and step 2 (the specified central angle)
Example 1:
Have students try #4-8 on CW.
Finding Arc Length:
Step 1: Use radius or diameter to find circumference.
Step 2: Divide circumference by # of equal pieces/slices
Example 3:
A circular pie is sitting in a pie tin and its diameter
is 8 inches across. The pie has 6 slices cut at equal
angles through the center of the pie. When you take
one piece of pie from the pie tin, what is the
approximate length of the exposed side of the pie
tin?
Example 4:
To build a circular stain glass window, a series of
circular pieces that are each 18 cm in diameter are
cut into 10 pieces with equal angles. The pieces are
rearranged into a multicolored circle. An iron
border is places around the circle. What is the
approximate length of the iron border along one
slice of glass?
Example 5:
The minute hand and the hour hands on a clock
originate at the center of the clock and reach to the
outer edge of the clock. The circumference of the
clock is 40 inches. When it is 6:00 pm, what is the
length of the arc created by the minute hand and
the hour hand?
Example 6:
The minute hand and the hour hands on a clock
originate at the center of the clock and reach to the
outer edge of the clock. When it is 2:00 pm, what is
the length of the arc created by the minute hand
and the hour hand?
STAY READY.
CW#35: Find Arc LENGTH
Geometry
*CLASSROOM COPY – DO NOT WRITE ON THIS!*
CRS
Objective
PPF 703 – Use relationships among circles, arcs, and distances in circles
13.3 Find length of arcs
Yesterday, we found arc MEASURE:
2) Solve for x. Assume that lines which appear to be diameters are actual diameters.
Today, we will find the LENGTH of an arc.
1) The circumference of a circle is 22 cm. what is
the diameter?
2) The radius of a circle is 2.5 cm. What is the
circumference?
3) The diameter of a circle is 15 mm. What is the
circumference?
4) Find the arc length of AB.
5) Find the arc length of AB.
6) A birthday cake is sliced into 8 equal pieces. The
arc length of one piece of cake is 6.28 inches as
shown. Find the diameter of the cake.
STAY READY.
7) Find the indicated measures.
8) Find the circumference of circle Q.
a. Find the length of arc FG.
b. Find the length of arc EFG.
Find the radius of circle Q.
c. Find the length of arc EHG.
9) A pizza is sitting in a circular box that fits its
edges exactly. The pizza has a diameter that is 9
inches across. The pizza has 8 equal slices cut at
equal angles through the center of the pizza. When
you take one piece of pizza from the circular pizza
box, what is the approximate length of the exposed
side of the box?
10) A circular pie is sitting in a pie tin and its
diameter is 7 inches across. The pie has 12 slices
cut at equal angles through the center of the pie.
When you take one piece of pie from the pie tin,
what is the approximate length of the exposed side
of the pie tin?
11) A pizza is sitting in a circular box that fits its
edges exactly. The pizza has a diameter that is 14
inches across. The pizza has 8 equal slices cut at
equal angles through the center of the pizza. When
you take one piece of pizza from the circular pizza
box, what is the approximate length of the exposed
side of the box?
12) The minute hand and the hour hands on a clock
originate at the center of the clock and reach to the
outer edge of the clock. When it is 4:00 pm, what is
the length of the arc created by the minute hand
and the hour hand?
13) The minute hand and the hour hands on a clock
originate at the center of the clock and reach to the
outer edge of the clock. The length of each hand is 6
inches. When it is 3:00 pm, what is the length of the
arc created by the minute hand and the hour hand?
14) The minute hand and the hour hands on a clock
originate at the center of the clock and reach to the
outer edge of the clock. When it is 2:00 pm, what is
the length of the arc created by the minute hand
and the hour hand?
15) The figure shows the stars in the Betsy Ross flag.
a.
b.
STAY READY.
16)
17)
18)
EXIT SLIP:
1) Find the length of arc AB.
2) The minute hand and the hour hands on a clock
originate at the center of the clock and reach to the
outer edge of the clock. The length of each hand is 4
inches. When it is 9:00 pm, what is the length of the
arc created by the minute hand and the hour hand?
3) What is the difference between arc measure and arc length?
4) What information is necessary to find arc length? Why?
STAY READY.