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Applying Area of Circles: IM 7.3.9

IM 6 – 8 Math, GeoGebra Classroom Activities, Aug 18, 2020

[url=https://im.kendallhunt.com/MS/teachers/2/3/9/preparation.html]“Applying Area of Circles”[/url] from IM Grade 7 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].

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Lesson 7.3.9

1. IM 7.3.9 Lesson: Applying Area of Circles

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IM 7.3.9 Lesson: Applying Area of Circles

The area of this field is about 500,000 m².

What is the field’s area to the nearest square meter? Assume that the side lengths of the square are exactly 800 m.

502,400[math]m^2[/math] 502,857[math]m^2[/math] 502,656[math]m^2[/math] 502,655[math]m^2[/math] 502,640[math]m^2[/math]

Each square has a side length of 12 units.

Compare the areas of the shaded regions in the 3 figures. Which figure has the largest shaded region? Explain or show your reasoning.

Each square in Figures D and E has a side length of 1 unit. Compare the area of the two figures. Which figure has more area? How much more? Show your reasoning or explain below.

Compare the area of the two figures. Which figure has more area? How much more? Explain or show your reasoning.

Which figure has a longer perimeter, Figure D or Figure E? How much longer?

The field inside a running track is made up of a rectangle 84.39 m long and 73 m wide, together with a half-circle at each end. The running lanes are 9.76 m wide all the way around. Use this applet to answer the below question.

What is the area of the running track that goes around the field?[i] Explain [/i]your reasoning here.

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Practice 7.3.9

1. IM 7.3.9 Practice: Applying Area of Circles

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IM 7.3.9 Practice: Applying Area of Circles

A circle with a 12-inch diameter is folded in half and then folded in half again. What is the area of the resulting shape?

Find the area of the shaded region. Express your answer in terms of π.

The face of a clock has a circumference of 63 in. What is the area of the face of the clock?

Which of these pairs of quantities are proportional to each other?

Diameter and area of a circle Radius and diameter of a circle Diameter and circumference of a circle Radius and area of a circle Radius and circumference of a circle

For the quantities above that you selected, what is the constant of proportionality for each?

Find the area of this shape in two different ways. Show your reasoning.

Elena and Jada both read at a constant rate, but Elena reads more slowly. For every 4 pages that Elena can read, Jada can read 5. Complete the table.

Here is an equation for the table: [math]j=1.25e[/math]. What does the 1.25 mean?

Write an equation for this relationship that starts [math]e=[/math]....

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