Mathematics

Question

Please help asap!!!!!!!!!!!
Please help asap!!!!!!!!!!!

2 Answer

  • ANSWER

    [tex]16\pi \: sq.in[/tex]

    EXPLANATION

    The area of a sector is calculated using the formula,

    [tex]Area = \frac{arc \: measure}{360 \degree} \times \pi {r}^{2} [/tex]

    The arc measure is given as 45°

    The radius of the circle is 8 inches.

    We substitute to obtain,

    [tex]Area = \frac{45 \degree}{360 \degree} \times \pi \times {8}^{2} [/tex]

    [tex]Area = \frac{1}{4} \times 64\pi = 16\pi[/tex]

  • Hello!

    The answer is:

    The correct option is the second option:

    [tex]SectorArea=8\pi in^{2}[/tex]

    Why?

    To answer the question, we need to calculate the total area of the circle (which corresponds to 360°) and then, calculate the equivalent area to the sector of the arc that measures 45°

    Calculating the total area, we have:

    [tex]TotalArea=\pi radius^{2} \\\\TotalArea=\pi 8^{2} =64\pi in^{2}[/tex]

    Now, we need to consider that the calculated area (total area) correspondes to all 360° that conforms the interior angle of a circle, now, if we want to calculate the area that represents a sector of the arc that measures 45°, we have to use the following formula:

    [tex]SectorArea=\frac{360\°}{45\° }*TotalArea\\\\SectorArea=\frac{45\°}{360\° }*64\pi in^{2}=\frac{1}{8} *64\pi in^{2}\\\\SectorArea=8\pi in^{2}[/tex]

    Hence, we have that the correct option is the second option:

    [tex]SectorArea=8\pi in^{2}[/tex]

    Have a nice day!

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