1. Find the area of each sector. Give your answer in two forms. 1) in terms of it and 2) using 3.14 for it. Round all answers to the nearest tenth.

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 = × π r², where

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 = × 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 = × 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

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