Applying Area of Circles

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Find Area

Solve the following problems to demonstrate your understanding of area and circumference.

(1). 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.

(2). 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.

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

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Exploring More on Area and Circumference of a Circle.

This is an exercise to show how the area and circumference of a circle change as the radius changes. Move the slider and observe.

Move the slider slowly and try to find values of the radius where the area is equal to the circumference.

How many values did you find?

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Circumference and Area (Exercise).

Use the applet below to answer the questions that follow.

What is the area and circumference of a circle when the radius is

(1). 1 cm

(2). 1.5 cm

(3). 3 cm

(4). 3.6 cm

(5). 4 cm

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

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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.

Drag the slider slowly and try to find values of the radius that make the area and circumference equal.

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