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Find the aree of the sector.
A.
(57 pi)/(8)
B.
(245 pi)/(3)
C
23520 pi
D.
(196 pi)/(3)

Find the aree of the sector. $\newline$ A. $\frac{57 \pi}{8}$ $\newline$ B. $\frac{245 \pi}{3}$ $\newline$ C $23520 \pi$ $\newline$ D. $\frac{196 \pi}{3}$

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Sum of finite series not start from 1

Full solution

Q. Find the aree of the sector.

\newline

A.

\frac{57 \pi}{8}

\newline

B.

\frac{245 \pi}{3}

\newline

C

23520 \pi

\newline

D.

\frac{196 \pi}{3}

Sector Area Formula: The area of a sector is given by the formula $A = (\frac{\theta}{360}) \cdot \pi \cdot r^2$ , where $\theta$ is the central angle in degrees and $r$ is the radius of the circle.
Radius and Central Angle: We need to find the radius $r$ and the central angle $\theta$ for each option to calculate the area of the sector.
Option A Area: For option A, the area is $(57\pi)/8$ . This looks like the area is already calculated, so no need to find radius or angle.
Option B Area: For option B, the area is $(\frac{245\pi}{3})$ . Again, this seems like the area is given directly.
Option C Area: Option C gives $23520\pi$ as the area, which also appears to be the final area.
Option D Area: Option D is $(196\pi)/3$ , and like the others, it's presented as the final area.
Comparison of Areas: Since all options are given in terms of $\pi$ , we don't need to use the value of $\pi$ for comparison.
Largest Area: Compare the coefficients of $\pi$ to determine the largest area: $\frac{57}{8}$ , $\frac{245}{3}$ , $23520$ , and $\frac{196}{3}$ .
Largest Area: Compare the coefficients of $\pi$ to determine the largest area: $\frac{57}{8}$ , $\frac{245}{3}$ , $23520$ , and $\frac{196}{3}$ .It's clear that $23520$ is much larger than the other coefficients.
Largest Area: Compare the coefficients of $\pi$ to determine the largest area: $\frac{57}{8}$ , $\frac{245}{3}$ , $23520$ , and $\frac{196}{3}$ . It's clear that $23520$ is much larger than the other coefficients. Therefore, the largest area of the sector is given by option C, which is $23520\pi$ .

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