$\"\"$

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(a)

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The surface is the machine part of the region between the graphs of $\"\"$ and $\"\"$ .

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$\"\"$

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The equation is $\"\"$ .

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Compare with the circle equation.

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Radius of the circle is $\"\"$ .

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From pythogorean theorem,

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$\"\"$

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$\"\"$

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(b).

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Area of the surface of the machine part is calculated by $\"\"$ .

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Area of the square is $\"\"$ .

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Central angle of the sector is $\"\"$ .

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$\"\"$

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$\"\"$

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Area of the machine part is $\"\"$ .

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Area of the surface of the machine part is $\"\"$ .

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$\"\"$

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$\"\"$

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(c).

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Area of the surface of the machine part as a function of radius $\"\"$ of the circle.

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$\"\"$

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Area of the surface of the machine part as a function of radius $\"\"$ of the circle is $\"\"$ .

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$\"\"$

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(a).

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The value of $\"\"$ is $\"\"$ .

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(b)

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Area of the surface of the machine part is $\"\"$ .

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(c).

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Area of the surface of the machine part as a function of radius $\"\"$ of the circle is $\"\"$ .