Question

What is the best estimate of the shaded area of the model in the picture? Use 3 for Pi.

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: State the formula for the area of a circle

$\begin{gathered} \text{Area}=\pi r^2 \\ r=\frac{diameter}{2} \end{gathered}$

STEP 2: Write the formula for finding the area of the shaded area

$\text{Area of shaded portion=Area of the whole circle - Area of the small white circle}$

STEP 3: Calculate the area of the whole circle

$\begin{gathered} \text{Area}=\pi r^2 \\ r=\frac{d}{2},d\text{ for the big circle is 6} \\ r=\frac{6}{2}=3 \\ \text{Area}=\pi\times3^2=\pi\times9=28.27433388 \end{gathered}$

STEP 4: Calculate the area for the smaller circle

$\begin{gathered} \text{Area}=\pi r^2 \\ r=\frac{d}{2},d\text{ for the smaller inner circle is }2 \\ r=\frac{2}{2}=1 \\ \text{Area}=\pi\times1\times1=\pi=3.141592654 \end{gathered}$

STEP 5: Calculate the shaded area of the model

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