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zlopas [31]
3 years ago
10

HELP PLEASE 100 POINTS PLUS BRAINLIEST, (I had the answers already but some reason they got deleted

Mathematics
1 answer:
Bas_tet [7]3 years ago
3 0

Answer:

\mathrm{11.\:}\frac{176}{5}\pi\:\mathrm{ft^2},\\\\\mathrm{12.\:}\frac{1573}{18}\pi\:\mathrm{mi^2},\\\\\mathrm{13.\:}\frac{269.08}{24}\pi\:\mathrm{km^2}\\\\\mathrm{14.\:}\frac{252.05}{6}\pi\:\mathrm{cm^2}\\\\\mathrm{15.\:}\frac{870.75}{72}\pi\:\mathrm{yd^2}\\\\\mathrm{16.\:}\frac{5953.48}{36}\pi\:\mathrm{m^2}

Step-by-step explanation:

The area of a sector can be given as:

\frac{c^{\circ}}{360^{\circ}}\cdot r^2\pi, where c is the angle of the sector in degrees.

<u>Problem 11:</u>

\frac{88^{\circ}}{360^{\circ}}\cdot 12^2\pi=\fbox{$\frac{176}{5}\pi\:\mathrm{ft^2}$}

<u>Problem 12:</u>

\frac{260^{\circ}}{360^{\circ}}\cdot 11^2\pi=\fbox{$\frac{1573}{18}\pi\:\mathrm{mi^2}$}

<u>Problem 13:</u>

Convert radians to degrees:

\frac{7\pi}{12}\cdot\frac{180}{\pi}=105^{\circ}

\frac{105^{\circ}}{360^{\circ}}\cdot 6.2^2\pi=\fbox{$\frac{269.08}{24}\pi\:\mathrm{km^2}$}

<u>Problem 14:</u>

Convert radians to degrees:

\frac{5\pi}{3}\cdot \frac{180}{\pi}=300^{\circ}

\frac{300^{\circ}}{360^{\circ}}\cdot 7.1^2\pi=\fbox{$\frac{252.05}{6}\pi\:\mathrm{cm^2}$}

<u>Problem 15:</u>

\frac{215^{\circ}}{360^{\circ}}\cdot 4.5^2\pi=\fbox{$\frac{870.75}{72}\pi\:\mathrm{yd^2}$}

<u>Problem 16:</u>

Convert radians to degrees:

\frac{13\pi}{18}\cdot\frac{180}{\pi}=130^{\circ}

\frac{130^{\circ}}{360^{\circ}}\cdot 21.4^2\pi=\fbox{$\frac{5953.48}{36}\pi\:\mathrm{m^2}$}

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