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# The central angle of a sector of a circle with radius 20 cm is 65°. Determine the area of the sector??

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- PuzzlingLv 71 year agoFavorite Answer
Let's first imagine that the question asked for the area of the full circle.

A = πr²

A = π(20 cm)²

A = 500π cm²

A ≈ 1257 cm²

But you don't want the full 360°, you just want a sector that is 65°, so multiply by the fraction:

Asector = 65/360 * A

Asector = 13/72 * A

Asector = 13/72 * 1257 cm²

≈ 227 cm²

- ted sLv 71 year ago
from circle being π radius ² = angle divide by 2 radius² we see the answer is [ ( 65 / 180) / 2 ] π ( 20²)

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