Grade 7 | Unit 3 | Lesson 9: Applying Area of Circles | Practice Problems

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?

• \(9\pi\) in2, about 28 in2

• 12\pi in2

• 15\pi in2

• 18\pi in2

• 6\pi in2

Find the area of the shaded region. Express your answer in terms of \(\pi\). Description: A shaded rectangle with three unshaded circles stacked one above the other inside the rectangle. The horizontal length of the rectangle is 18 inches. On the right side of the rectangle, the length of the vertical side is subdivided into 4 different lengths using arrows. The first arrow indicates that the distance from the top of the rectangle to the top of the first circle is 3 inches. The second arrow indicates that the distance from the top to the bottom of the first circle is 6 inches. The third arrow indicates that the distance from the top to the bottom of the second circle is 9 inches. The fourth arrow indicates that the distance between the top to the bottom of the third circle is 12 inches.

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

• 316 in2

• 300 in2

• 280 in2

• 350 in2

• 250 in2

Which of these pairs of quantities are proportional to each other? For the quantities that are proportional, what is the constant of proportionality?

• Radius and diameter of a circle - Yes, constant is 2 or \(\frac12\)

• Radius and circumference of a circle - Yes, constant is \(2\pi\) or \(\frac{1}{2\pi}\)

• Radius and area of a circle - No

• Diameter and circumference of a circle - Yes, constant is \(\pi\) or \(\frac{1}{\pi}\)

• Diameter and area of a circle - No

Find the area of this shape in two different ways.

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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.

Pages read by Elena	Pages read by Jada
4	5
1	\(\frac{5}{4}\) or 1.25
9	\(\frac{45}{4}\) or 11.25
e	\(\frac{5}{4} e\) or \(1.25e\)

12 pages read by Jada leads to 15 pages read by Elena. Find the equation for \(e\).

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