Question

The measure of central angle XYZ is 1.25 pi radians.

What is the area of the shaded sector?
$0/2\pi (\pi r^2)$
[tex]x/360(\pi r^2)
10 units2

20 units2

40 units2

80 units2

Answer 1

Solution :----

→ π radian = 180°

→ 1.25 π radian = 1.25 * 180° = 225°

Now,

→ Radius = 8cm.

→ Angle XYZ = 225° .

→ So, Exterior Angle of XYZ = 360° - 225° = 135° .

→ Area of shaded sector = (@/360°) * π * r²

Putting Values we get :-

→ Area of shaded sector = (135°/360°) * (22/7) * (8)²

→ Area of shaded sector = 0.375 * 3.14 * 64

→ Area of shaded sector = 75.36cm.²

Hence, Area of Shaded Region is 75.36cm².

i dont know the answer .. Delete it if you think its wrong . Thank you.

when central angle is given 1.25π radian. what should i will take. we have to Find Shaded Area . And this is (2π - 1.25π Radian ).

Either we do This or , we can find Area by (1.25π radian) and than subtract it from whole circle area.

Answer 2

GiveN :

• ∠XYZ (interior) = 1.25 π rad
• Radius (r) = 8 units

To FinD :

• Area of the shaded Region

SolutioN :

Angle is 1.25 πrad = 180 * 1.25 = 225°

• Angle (θ) is 225°

Now, use formula for sector

$\dashrightarrow \large{\boxed{\tt{Area \: = \: \frac{\theta}{360} \: \pi \: r^2}}} \\ \\ \dashrightarrow \tt{Area \: = \: \dfrac{225}{360} \times 3.14 \times (8)^2} \\ \\ \dashrightarrow \tt{Area \: = \: \dfrac{225}{\cancel{360}} \times 3.14 \times \cancel{64}} \\ \\ \dashrightarrow \tt{Area \: = \: \dfrac{\cancel{225}}{\cancel{45}} \times 3.14 \times 8} \\ \\ \dashrightarrow \tt{Area \: = \: 5 \times 25.12} \\ \\ \dashrightarrow \tt{Area \: = \: 125.6 \: unit^2} \\ \\ \large{\underline{\boxed{\sf{Area \: = \: 125.69 \: unit^2}}}}$