In the figure below, the rectangle in the top left corner measures 3 cm by 6 cm.
What is the radius and area of the circle? What is the area of the square?
Solution:
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Using the Pythagorean Theorem in the figure to the right, we have: |
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(r – a)2 + (r – b)2 = r2. Plugging in a = 3 and b = 6, we have: (r – 3)2 + (r – 6)2 = r2 i.e. r2 – 18r + 45 = 0. |
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Factoring, we have: (r – 15)(r – 3) = 0. The radius of the circle cannot be equal to 3 (looking at the picture, this would not make any sense, since we have the width of the box above is already 6 cm). Thus, r = 15 cm. Since the radius is 15 cm, the area of the circle is given by 225p cm2. And since the radius of the circle is 15 cm, the diameter of the circle (and length of each side of the square) is 30 cm. Thus, the area of the square is 30*30 = 900 cm2. |
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