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    Question

    A circle inscribed in a square has a diameter of 14 cm.

    If a smaller square is inscribed within this circle, calculate the area of the smaller square. Also, find the area of the region between the two squares.
    A Area of smaller square = 98 cm², Area of region = 98 cm² Correct Answer Incorrect Answer
    B Area of smaller square = 98 cm², Area of region = 55 cm² Correct Answer Incorrect Answer
    C Area of smaller square = 100 cm², Area of region = 55 cm² Correct Answer Incorrect Answer
    D Area of smaller square = 96 cm², Area of region = 58 cm² Correct Answer Incorrect Answer

    Solution

    The diameter of the circle is 14 cm, so its radius is 7 cm.  The diagonal of the smaller square is equal to the diameter of the circle, which is 14 cm. Using the formula for the diagonal of a square (d = a√2),  where a is the side of the square, we find that the side of the smaller square is a = 14/√2 = 7√2. Area of smaller square = (7√2)² = 98 cm². Area of larger square = 14² = 196 cm². Area of the region = 196 - 98 = 98 cm². Correct answer: a) Area of smaller square = 98 cm², Area of region = 98 cm²

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