Section B Section B Checkpoint

Problem 1

Lin measured the diameter and circumference of a circle. Then she used her measurements to calculate the area.

Han measured the diameter and circumference of a different circle.

	diameter (in)	circumference (in)	area (in²)
Lin’s circle	6	19	28.5
Han’s circle	3	9.5	?

Han thinks the area of his circle is 14.25 in². Do you agree? Explain or show your reasoning.

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Solution

Sample responses:

No, the area of a circle is not proportional to the diameter. Since the diameter of Han’s circle is one-half the diameter of Lin’s circle, the area of Han’s circle will be $(\frac12)^2$ the area of Lin’s circle.
No, the area of Han’s circle is about 7 in². Possible strategies:
- The radius is 1.5 inches because $3 \div 2 = 1.5$ .
  $\text{Area} = \frac12 \text{circumference} \boldcdot \text{radius}$
  $\text{Area} = \frac12 (9.5) \boldcdot (1.5)$
  $\text{Area} = 7.125$
- The radius is 1.5 inches because $3 \div 2 = 1.5$ .
  $A = \pi r^2$
  $A = 3.14 * (1.5)^2$
  $A = 7.065$

Show Sample Response

Sample Response

Sample responses:

No, the area of a circle is not proportional to the diameter. Since the diameter of Han’s circle is one-half the diameter of Lin’s circle, the area of Han’s circle will be $(\frac12)^2$ the area of Lin’s circle.
No, the area of Han’s circle is about 7 in². Possible strategies:
- The radius is 1.5 inches because $3 \div 2 = 1.5$ .
  $\text{Area} = \frac12 \text{circumference} \boldcdot \text{radius}$
  $\text{Area} = \frac12 (9.5) \boldcdot (1.5)$
  $\text{Area} = 7.125$
- The radius is 1.5 inches because $3 \div 2 = 1.5$ .
  $A = \pi r^2$
  $A = 3.14 * (1.5)^2$
  $A = 7.065$

What is the area of the shaded region?

$3\pi$ square units

$9\pi$ square units

$12\pi$ square units

$36\pi$ square units

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Solution

$9\pi$ square units

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Sample Response

$9\pi$ square units