Question

Shaded area is 40 pi cm squared. Find r

Answer 1

Answer:

$A =\frac{x \pi r^{2} }{360}$

Step-by-step explanation:

A = 40π

x is the angle of sector = 144°

r = ? unknown

 Substituting the values in formula

40π = 144° π $r^{2}$ / 360°

On simplification we get

110 = $r^{2}$

r = 10.48cm

Answer 2

Answer: r = 10 cm

Step-by-step explanation:

The formula for determining the area of a sector is expressed as

expressed as

Area of sector = θ/360 × πr²

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

θ = 144°

Area of sector = 40π

Therefore,

40π = 144/360 × π × r²

40π × 360 = 144 × π × r²

14400π = 144πr²

Dividing through by π, it becomes

1440 = 144r²

r² = 14400/144

r² = 100

r = √100

r = 10 cm