Question

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Answer 1

Step-by-step explanation:

1). R=6cm

AB=6π

=> 2πR(∅/360) = 6π

=> ∅ = 120°

2). AREA OF SECTOR = πr²(∅/360)

=> kπ cm² = π ×9×9×(120/360)

=> kπ = 27π

=> k= 27cm²

Answer 2

Answer

$\alpha = \frac{2\pi}{3} and \: k = 27$

step-by-step explanation:

The circumference of a circle of radius(r), which is an arc subtending an angle of 2π is 2πr.

So if the angle subtended by an arc is alpha then the lenth of the arc is

$r \alpha$

the area of circle of radius r ,which is a sector subtending an angle of 2π is

$\pi {r}^{2} = \frac{1}{2} (2\pi) {r}^{2}$

So if the angle subtended by a sector is

$\alpha$

then the area of the sector is

$\frac{1}{2} \alpha {r}^{2}$

In our example, we have r=9 cm and length of

arc = 6πcm

so (in cm ) we have ,

$9 \alpha = 6\pi \\ \alpha = \frac{6\pi}{9} = \frac{2\pi}{3}= 120°$

Then the area (in cm² ) of the sector is:

$k\pi = \frac{1}{2} \alpha {r}^{2} = \frac{1}{2} (\frac{2\pi}{3} )( {9}^{2} ) = 27\pi$

so

$k = 27$

I hope it helps you

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