Semicircle area?

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Semicircle area?

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Answer 1 · 2017-05-08T03:55:59

The area of the shaded section is $113.076 m m^{2}$ $113.076mm^2$ .

Explanation:

To calculate the area of the shaded area, we calculate the difference between the area of the semicircle and the area of the circle.

The formula for area of the semicircle is:

$A_{S} = \frac{π r_{S}^{2}}{2}$ $A_S=(pir_S^2)/2$ , where $A_{S} =$ $A_S=$ Area of semi-circle, and $r_{S}^{2} =$ $r_S^2=$ radius of semicircle, given as $12 m m$ $12mm$ (since $24 m m$ $24mm$ is the diameter which is twice the radius).

The formula for area of the circle is:

$A_{C} = π r_{C}^{2}$ $A_C=pir_C^2$ , where $A_{C} =$ $A_C=$ Area of circle, and $r_{C}^{2} =$ $r_C^2=$ radius of circle, calculated as $6 m m$ $6mm$ (since the radius of the semicircle forms the diameter of the circle, as can be seen in the diagram).

Hence, to calculate the difference between the two, we write:

$A_{S} - A_{C} = \frac{π r_{S}^{2}}{2} - π r_{C}^{2}$ $A_S-A_C=(pir_S^2)/2-pir_C^2$

$A_{S} - A_{C} = \frac{π \times 12^{2}}{2} - π \times 6^{2}$ $A_S-A_C=(pixx12^2)/2-pixx6^2$

$A_{S} - A_{C} = \frac{π \times 144}{2} - π \times 36$ $A_S-A_C=(pixx144)/2-pixx36$

$A_{S} - A_{C} = (π \times 72) - (π \times 36)$ $A_S-A_C=(pixx72)-(pixx36)$

$A_{S} - A_{C} = π (72 - 36)$ $A_S-A_C=pi(72-36)$

$A_{S} - A_{C} = π \times 36$ $A_S-A_C=pixx36$

We consider the value of $π$ $pi$ as $3.141$ $3.141$ .

$A_{S} - A_{C} = 3.141 \times 36$ $A_S-A_C=3.141xx36$

$A_{S} - A_{C} = 113.076$ $A_S-A_C=113.076$

Since the given diameter is in millimetres, the area will be expressed as square millimetres or $m m^{2}$ $mm^2$ .

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Semicircle area?

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