Question

1. a circle with an 8 - inch radius is folded in half and then folded in half again. what is the area of the resulting shape? express your answer in terms of π.

Explanation:

Step1: Calculate the area of the original circle

The area formula of a circle is \(A = \pi r^{2}\). Given \(r = 8\) inches, so \(A=\pi\times8^{2}=64\pi\) square - inches.

Step2: Analyze the effect of folding

Folding the circle in half once divides the area by 2. Folding it in half again divides the resulting area by 2. In total, the area of the resulting shape is \(\frac{1}{2}\times\frac{1}{2}\) of the original circle's area.

Step3: Calculate the area of the resulting shape

Let \(A_{new}\) be the area of the resulting shape. Then \(A_{new}=\frac{1}{4}\times A\). Substitute \(A = 64\pi\) into the formula: \(A_{new}=\frac{1}{4}\times64\pi = 16\pi\) square - inches.

Answer:

\(16\pi\) square - inches