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An american man wants to break the guinness Record or largest pizza. He manages to bake with a radius of 66 feet. he offers to feed his town. if he cuts a slice with a central angle of 37* , how much area would this slice cover?

Sagot :

sqdancefan

Answer:

  4418.6 square feet

Step-by-step explanation:

The area of a sector of a circle is given by the formula ...

  A = 1/2r²θ . . . . where r is the radius, and θ is the central angle in radians

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The area of the proposed pizza slice is the area of a sector with a radius of 66 ft and a central angle of 37°. That area will be ...

  A = 1/2(66 ft)²(37°×π/180°) ≈ 4418.6 ft²

The pizza slice would cover 4,418.6 square feet.

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Additional comment

There are 2π radians in the 360° of a circle. That means ...

  1 radian = 180°/π ≈ 57.296°

  1° = π/180 radians

As we have done above, the number of radians can be found by multiplying the degree measure by π/180°. The units of degrees will cancel, leaving a "pure number" with no units. That is, "radians" is a non-unit: a number of radians is a pure number.

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