A circle is inscribed within a square with a side length of 18 cm. Find the area of the part of the square not covered by the circle.
69.53 cm²
The uncovered region is what remains of the square after the inscribed circle is cut away, so we compute the square's area and the circle's area and subtract the second from the first.
The side of the square is 18 cm, so its area is \(18^{2} = 324\ \text{cm}^{2}\).
A circle inscribed in a square touches all four sides, so its diameter equals the side of the square, 18 cm, giving a radius of \(\frac{18}{2} = 9\) cm.
The area of the circle is \(\pi r^{2} = \pi \times 9^{2} = 81\pi\ \text{cm}^{2}\).
Taking \(\pi \approx 3.1416\), this is \(81 \times 3.1416 \approx 254.47\ \text{cm}^{2}\).
The area not covered by the circle is the difference \(324 - 254.47 = 69.53\ \text{cm}^{2}\). This leftover is the four corner pieces of the square that the circle cannot reach.
Key concept: for a circle inscribed in a square the diameter equals the side, so radius = side ÷ 2, and uncovered area = area of square − area of circle. The area not covered is 69.53 cm².
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