Question

find the width of radius r if the width w of the shaded region is 2cm and its area is 176cm^2, use 22/7 for pi (its a full circle)

Answer 1

The area of a shape is the amount of space it can occupy.

The value of r is 13

From the question (see attachment), we have:

$\mathbf{A =176}$ --- area of the shaded region

$\mathbf{w = 2}$ --- the width of the shaded region

The area of the complete circle would be:

$\mathbf{A_1 =\pi (r + w)^2}$

The area of the small circle is:

$\mathbf{A_2 =\pi r^2}$

So, the area of the shaded region is:

$\mathbf{A = A_1 - A_2}$

Substitute known values

$\mathbf{176 =\pi (r + w)^2 - \pi r^2 }$

Substitute 2 for w

$\mathbf{176 =\pi (r + 2)^2 - \pi r^2 }$

Expand

$\mathbf{176 =\pi (r^2 + 4r + 4) - \pi r^2 }$

Open brackets

$\mathbf{176 =\pi r^2 + 4\pi r + 4\pi - \pi r^2 }$

Cancel out line terms

$\mathbf{176 =4\pi r + 4\pi }$

Divide through by 4

$\mathbf{44 =\pi r + \pi }$

Factor out pi

$\mathbf{44 =\pi(r+ 1) }$

Divide through by pi

$\mathbf{r + 1= \frac{44}{ \pi} }$

Substitute 22/7 for pi

$\mathbf{r + 1= \frac{44}{ 22/7} }$

Using a calculator, we have

$\mathbf{r + 1= 14}$

Solve for r

$\mathbf{r= 14 -1}$

$\mathbf{r= 13}$

Hence, the value of r is 13

Read more about areas of circles at:

brainly.com/question/23328170