using circumference, arc lengths, perimeter and area in the real world

MM2G3 Students will understand properties of circles.

MM2G3 c Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

Using Circumference, Arc Lengths, Perimeter and Area in the Real World

How do we solve real world problems?

M2 Unit 3: Day 11

Lesson 6.7 and 6.8

Thursday, April 20, 2023



Find the area of the shaded region.

A(shaded) = A(circle) – A(square) = (15² ) – (15√2*15√2) = (225 ) – (450) = 114.16 m²

A(shaded) = A(square) – A(16 circles) = 576 – 16 (9 ) = 123.6 cm²

1. 2.

24 cm

24 cm15

P

PP



Find the perimeter of the region.

138.56 in

3.



2827 cm

Thread A spool of thread contains 150 revolutions of thread. The diameter of the spool is 3 centimeters. Find the length of the thread to the nearest centimeter.

4.

6 cm



A pizza is cut into 10 equal slices. The arc length of one piece of pizza is 4 in. Find the circumference of the pizza.

4 3636040

inCC in°

=°

=

5.



The dimensions of a car tire are shown at the right. To the nearest foot, how far does the tire travel when it makes 15 revolutions?

STEP 1 Find the diameter of the tire

STEP 2 Find the circumference of the tire

Tire Revolutions

SOLUTION

d = 15 + 2 (5.5) = 26 in.

C = πd = π(26) ≈ 81.68 in.

Find distance traveled

6.



EXAMPLE 2Use circumference to find distance traveled

STEP 3 Find the distance the tire travels in 15 revolutions. In one revolution, the tire travels a distance equal to its circumference. In 15 revolutions, the tire travels a distance equal to 15 times its circumference.

15 81.68 in

= 1225.2 in

STEP 4 Use unit analysis. Change 1225.2 inches to feet.

1225.2 in. 1 ft

12 in.= 102.1 ft

The tire travels approximately 102 feet.ANSWER



GUIDED PRACTICE

7. A car tire has a diameter of 28 inches. How many revolutions does the tire make while traveling 500 feet?

SOLUTION

STEP 1 Find the circumference of the tire

C = πd = π(28) ≈ 87.92 in.

STEP 2 Use unit analysis. Change 500 feet to inches.

500 ft.12 in.

1 ft= 6000 in.



GUIDED PRACTICE

The tire makes 68.2 revolutions.ANSWER

STEP 3 Find the number of revolutions

N 87.926000

= 68.24N



A company receives an order for 65 pieces of fabric in the given shape. Each piece is to be dyed red. To dye 6 in2 of fabric, 2 oz of dye is needed. How much dye is needed for the entire order?

To find the area of the shape in square inches, divide the shape into parts.

The two half circles have the same area as one circle.

8.



The area of the circle is (1.5)2 = 2.25 in2.

The area of the square is (3)2 = 9 in2.

The total area of the shape is 2.25 + 9 ≈ 16.1 in2.

The total area of the 65 pieces is 65(16.1) ≈ 1044.5 in2.

The company will need 1044.5 ≈ 348 oz of dye for the entire order.

A company receives an order for 65 pieces of fabric in the given shape. Each piece is to be dyed red. To dye 6 in2 of fabric, 2 oz of dye is needed. How much dye is needed for the entire order?

8.



Homework: Page 229 # 24,25Page 233 # 28,29 Page 235 # 23,26,27

using circumference, arc lengths, perimeter and area in the real world

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