Respuesta :

cmrc78

Answer:

[tex]902.6mm^{2}[/tex] (highlighted) or [tex]3875.8mm^{2}[/tex] (shaded)

Step-by-step explanation:

Observe that the area of the whole circle is [tex]\Pi r^{2}[/tex] where r is 39mm. Note also that the whole circle is 360°. The area of OAB can therefore be calculated as the area of the full circle multiplied by the quotient representing the highlighted area compared to the full circle. Let's show what this means through calculations.

[tex]Area_{full circle} = \Pi * 39mm * 39mm = 1521mm^{2} * \Pi[/tex]

[tex]Area_{white arch} = Area_{full circle} * \frac{68^{o} }{360^{o}} =1521mm^{2} * \Pi * \frac{68^{o} }{360^{o}} \approx 902.6mm^{2}[/tex]

To calculate the complement (the shaded part) you could simply subtract the area of the white part from the full circle area.

[tex]1521mm^{2} * \Pi - (1521mm^{2} * \Pi * \frac{68^{o} }{360^{o}}) \approx 3875.8mm^{2}[/tex]

semsee45

Answer:

3875.8 mm²

Step-by-step explanation:

Angles around a point sum to 360°, so the central angle of the shaded major sector is:

[tex]360^{\circ}-68^{\circ}=292^{\circ}[/tex]

To find the area of the major sector OAB of circle O, we can use the area of a sector formula:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Area of a Sector}}\\\\A= \left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$A$ is the area.}\\\phantom{ww}\bullet\;\textsf{$r$ is the radius.}\\\phantom{ww}\bullet\;\textsf{$\theta$ is the central angle in measured in degrees.}\end{array}}[/tex]

Substitute θ = 292° and r = 39 into the formula, and solve for A:

[tex]A= \left(\dfrac{292^{\circ}}{360^{\circ}}\right) \pi \cdot 39^2[/tex]

[tex]A= \left(\dfrac{73}{90}\right) \pi \cdot 1521[/tex]

[tex]A= \dfrac{12447}{10} \pi[/tex]

[tex]A=3875.7828567...[/tex]

[tex]A=3875.8\; \sf mm^2\;(1\;d.p.)[/tex]

Therefore, the shaded area OAB is 3875.8 mm².

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