Answer:
1.
1) The area of the sector is 168.8π mi²
2) The area of the sector is 529.9 mi²
2.
1) The area of the sector is 42.3π in²
2) The area of the sector is 132.7 in²
Step-by-step explanation:
The formula of the area of a sector in a circle is A = [tex]\frac{x}{360}[/tex] × π r², where
- x is the central angle subtended by the arc of the sector
- r is the radius of the circle
1.
∵ The central angle subtended by the arc of the circle is 270°
∴ x = 270°
∵ The radius of the circle is 15 mi.
∴ r = 15
→ Substitute them in the formula of the area above
∵ A = [tex]\frac{270}{360}[/tex] × π (15)²
∴ A = 168.75π mi²
→ Round it to the nearest tenth
∴ A = 168.8π mi²
1) The area of the sector is 168.8π mi²
∵ π = 3.14
∴ A = 168.75 × 3.14
∴ A = 529.875 mi²
→ Round it to the nearest tenth
∴ A = 529.9 mi²
2) The area of the sector is 529.9 mi²
2.
∵ The central angle subtended by the arc of the circle is 90°
∴ x = 90°
∵ The radius of the circle is 13 in
∴ r = 13
→ Substitute them in the formula of the area above
∵ A = [tex]\frac{90}{360}[/tex] × π (13)²
∴ A = 42.25π in²
→ Round it to the nearest tenth
∴ A = 42.3π in²
1) The area of the sector is 42.3π in²
∵ π = 3.14
∴ A = 42.25 × 3.14
∴ A = 132.665 in²
→ Round it to the nearest tenth
∴ A = 132.7 in²
2) The area of the sector is 132.7 in²
