Question

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

Answer 1

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=(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=(d)/(2),d\text{ for the big circle is 6} \\ r=(6)/(2)=3 \\ \text{Area}=\pi*3^2=\pi*9=28.27433388 \end{gathered}`

STEP 4: Calculate the area for the smaller circle

`\begin{gathered} \text{Area}=\pi r^2 \\ r=(d)/(2),d\text{ for the smaller inner circle is }2 \\ r=(2)/(2)=1 \\ \text{Area}=\pi*1*1=\pi=3.141592654 \end{gathered}`

STEP 5: Calculate the shaded area of the model