Question

Please help dont understand!​

Answer 1

$\bold{Answer} \downarrow$

$Length\ of\ Arc\ ADB = \large\boxed{\frac{68\pi}{9} }$

$Area\ of\ shaded\ region= \large\boxed{\frac{136\pi}{9} }$

Formulas needed:

$Arc\ length=\boxed{2\pi r(\frac{\theta}{360} )}$

$Area \ of\ a\ sector=\boxed{(\frac{n}{360})\times\pi \times r^2}$

$Area\ of\ Circle=\boxed {\pi\times r^2}$

Step-by-step explanation:

First, let's find the arc length:

$Arc\ length=2\pi r(\frac{\theta}{360})$

$=2\pi (4)(\frac{340}{360})$

$=2\pi (4)(\frac{17}{18})$

$=2\pi(\frac{68}{18})$

$=\frac{136\pi }{18}$

$\longrightarrow \large\boxed{\frac{68\pi}{9} }$

Next, let's find the area of the sliver of the circle we just found the arc length of.

$Area \ of\ a\ sector=(\frac{n}{360})\times\pi \times r^2$

$=(\frac{20}{360} )\times \pi \times 4^2$

$=(\frac{1}{18})\times \pi \times 16$

$=\frac{16\pi}{18}$

$\longrightarrow \frac{8 \pi}{9}$

Finally, find the area of the entire circle and subtract the sliver area by that.

$Area\ of\ Circle= {\pi\times r^2$

$=\pi \times 4^2$

$\longrightarrow16\pi$

Subtracting the area by the sliver.

$Area\ of\ entire\ circle \ -\ Area\ of\ sliver\ of\ circle$

$=16\pi -\frac{8\pi}{9}$

$=\frac{144\pi}{9} -\frac{8\pi }{9}$

$\longrightarrow \large\boxed{\frac{136\pi}{9} }$

Answer 2

Answer:

Step-by-step explanation:

C = 2 π r

A = π r²

~~~~~~~~~~~

(1). C = 8 π

Let the length of the arc ADB is "x"

x = ( 8π ÷ 360° ) × 340°

x = $\frac{68}{9} \pi$

(2). A = 16 π

The area of shaded region is

( 16 π ÷ 360° ) × 340° = $\frac{136}{9} \pi$