1.

The measure of central angle XYZ is 1.25 pi radians.What is the area of the shaded sector?[tex]x/360(\pi r^2)10 units2 20 units240 units280 units2

Answer»

GiveN :

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

To FIND :

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}}}}


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