Question

A 3 cm×3 cm3cm×3cmstart color #1fab54, 3, start text, c, m, end text, times, 3, start text, c, m, end text, end color #1fab54 rectangle sits inside a circle with radius of 4 cm4cmstart color #11accd, 4, start text, c, m, end text, end color #11accd.What is the area of the shaded region? Round your final answer to the nearest hundredth.

Answer 1

The areas of the circle and rectangle are

`\begin{gathered} A_{\text{circle}}=r^2\cdot\pi=\pi(4)^2=16\pi \\ \text{and} \\ A_{\text{rectangle}}=lw=3\cdot3=9 \end{gathered}`

Therefore, the area of the shaded region is

`\Rightarrow A_{\text{shaded}}=A_(circle)-A_{\text{rectangle}}=16\pi-9=_{}41.2654\ldots\approx41.27`

The rounded answer is 41.27cm^2