Respuesta :

rambolokbrain

Answer:

To find the area of a sector, you can use the formula:

[tex][ \text{Area of sector} = \frac{\text{angle measure}}{360^\circ} \times \pi r^2 ][/tex]

Given that the radius ( r = 8 ) cm and the angle measure is ( 45^\circ ), you can plug these values into the formula:

[tex][ \text{Area of sector} = \frac{45^\circ}{360^\circ} \times \pi \times 8^2 ][/tex]

[tex][ = \frac{1}{8} \times \pi \times 64 ][/tex]

[tex][ = 8 \pi ][/tex]

So, the area of the sector is ( 8 \pi ) square centimeters.

semsee45

Answer:

Exact area = 8π cm²

Rounded area = 25.1 cm² (nearest tenth)

Step-by-step explanation:

To find the area of a sector where the central angle is measured in degrees, we can use the following 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{$r$ is the radius.}\\\phantom{ww}\bullet\;\;\textsf{$\theta$ is the angle measured in degrees.}\end{array}}[/tex]

In this case:

  • r = 8 cm
  • θ = 45°

Substitute the values into the formula and solve for area A:

[tex]A=\left(\dfrac{45^{\circ}}{360^{\circ}}\right) \pi \cdot 8^2\\\\\\A=\dfrac{1}{8} \pi \cdot 64\\\\\\A=8\pi\\\\\\A=25.1327412287...\\\\\\A\approx 25.1\; \sf cm^2[/tex]

Therefore, the exact area of the sector is 8π cm², which is approximately 25.1 cm² rounded to the nearest tenth.

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