Question

1. a square flooring tile has a circular design printed on it. if the tile is 20 cm long on each side, what is the area of the tile not covered by the design?

Explanation:

Step1: Calculate the area of the square

The area formula of a square is \(A = s^2\), where \(s\) is the side - length. Given \(s = 20\space cm\), then \(A_{square}=20\times20=400\space cm^{2}\).

Step2: Calculate the area of the circle

The diameter of the circle \(d = 20\space cm\), so the radius \(r=\frac{d}{2}=\frac{20}{2} = 10\space cm\). The area formula of a circle is \(A=\pi r^{2}\), taking \(\pi = 3.14\), then \(A_{circle}=3.14\times10^{2}=3.14\times100 = 314\space cm^{2}\).

Step3: Calculate the uncovered area

The uncovered area \(A = A_{square}-A_{circle}\). Substitute the values: \(A = 400 - 314=86\space cm^{2}\).

Answer:

\(86\space cm^{2}\)