Question

Question

Find the area of the shaded region in the figure below, if the diameter of the circle is 2 and the height of the rectangle is 8.
Use 3.14 for pi and round to the nearest hundredth.

Answer 1

the area of the shaded region is 14.43 square units

Step-by-step explanation

to solve this we need to subtrac the area of a half circle from the area of the rectangle, so

Step 1

find the areas

a) rectangle

the area of a rectangle is given by:

note that thewidth of the rectangle equals the diameter of the circle, so

`\begin{gathered} Area=2\text{ *8= 16 square units} \\ Area_(rectangle)=16\text{ \lparen un}^2) \end{gathered}`

b)half circle

the area of half circle is given by:

`Area_(halfcircle)=\pi((diamter^2)/(8))`

so, let

diameter = 2

and replace

`\begin{gathered} Area_(halfcircle)=3.14((2^2)/(8)) \\ Area_(halfcircle)=3.14*(1)/(2)=1.57 \\ Area_(halfcircle)=1.57\text{ \lparen un}^2) \end{gathered}`

Step 3

finally, subtract the areas, so

`16.-1.57=14.43`

so, the area of the shaded region is 14.43 square units

I hope this helps you