Question

below. approximately what percent of the circles area lies in the rectangle? 8 6 50.6% 55.5% 61.1% 64.6%

Explanation:

Step1: Calculate the area of the rectangle

The area formula for a rectangle is \(A = l\times w\). Given \(l = 8\) and \(w = 6\), then \(A_{rectangle}=6\times8 = 48\).

Step2: Calculate the diameter of the circle

Using the Pythagorean theorem \(d=\sqrt{6^{2}+8^{2}}\) (since the diagonal of the rectangle is the diameter of the circle). So \(d=\sqrt{36 + 64}=\sqrt{100}=10\), and the radius \(r=\frac{d}{2}=5\).

Step3: Calculate the area of the circle

The area formula for a circle is \(A=\pi r^{2}\). Substituting \(r = 5\), we get \(A_{circle}=\pi\times5^{2}=25\pi\approx25\times3.14 = 78.5\).

Step4: Calculate the percentage

The percentage is \(\frac{A_{rectangle}}{A_{circle}}\times100\%=\frac{48}{78.5}\times100\%\approx61.1\%\).

Answer:

61.1%