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Posted 2 months ago

A sector with a central angle measure of 175175^{\circ} has a radius of 12 cm12 \mathrm{~cm}.

What is the area of the sector?
Choose 1 answer:
(A) 353πcm2\frac{35}{3} \pi \mathrm{cm}^{2}
(B) 24πcm224 \pi \mathrm{cm}^{2}
(C) 70πcm270 \pi \mathrm{cm}^{2}
(D) 144πcm2144 \pi \mathrm{cm}^{2}
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Answer from Sia
Posted 2 months ago
Solution by Steps
step 2
First, we convert the central angle from degrees to radians. Since 180180^\circ is equivalent to π\pi radians, 175175^\circ is 175180π\frac{175}{180} \pi radians
step 3
Now we can substitute the values into the formula: A=12×122×175180π=12×144×175180πA = \frac{1}{2} \times 12^2 \times \frac{175}{180} \pi = \frac{1}{2} \times 144 \times \frac{175}{180} \pi
step 4
Simplifying the expression, we get A=72×175180π=35×πA = 72 \times \frac{175}{180} \pi = 35 \times \pi
step 5
The area of the sector is therefore 35π cm235 \pi \text{ cm}^2
Key Concept
Area of a Sector
The area of a sector is calculated by the formula A=12r2θA = \frac{1}{2} r^2 \theta, where the angle θ\theta must be in radians.

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