360 (pir²)...

KAntoineDoix

Verified answer

✒️SECTOR AREA

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$\large\underline{\mathbb{ANSWER}:}$

$\qquad \LARGE \:\: \rm 19.625 \: sq. \: cm.$

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$\large\underline{\mathbb{SOLUTION}:}$

Determine the area of the sector with the given formula.

$\rm A_{Sector} = \frac{m\overset{\frown}{PQ}}{360} \, \big(\pi r^2\big) \\$

$\rm A_{Sector} = \frac{90}{360} \, \big(\pi (5)^2\big) \: cm^2 \\$

$\rm A_{Sector} = \frac{90}{360} \, \big(\pi (5)^2\big) \: cm^2 \\$

$\rm A_{Sector} = \frac{\,1\,}{4} \, \big(25\pi \big) \: cm^2 \\$

$\rm A_{Sector} = \frac{\,25\pi\,}{4} \: cm^2 \\$

$\rm A_{Sector} = 6.25\pi \:cm^2\\$

Let 3.14 be the approximate value of pi.

$A_{Sector} \approx 6.25(3.14) \: cm^2$

$A_{Sector} \approx 19.625 \: cm^2$

Therefore, the area of the sector PTQ is approximately 19.625 sq. centimeters

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