Question

Math

Posted 2 months ago

```
A sector with a central angle measure of $175^{\circ}$ has a radius of $12 \mathrm{~cm}$.
What is the area of the sector?
Choose 1 answer:
(A) $\frac{35}{3} \pi \mathrm{cm}^{2}$
(B) $24 \pi \mathrm{cm}^{2}$
(C) $70 \pi \mathrm{cm}^{2}$
(D) $144 \pi \mathrm{cm}^{2}$
```

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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 $180^\circ$ is equivalent to $\pi$ radians, $175^\circ$ is $\frac{175}{180} \pi$ radians

step 3

Now we can substitute the values into the formula: $A = \frac{1}{2} \times 12^2 \times \frac{175}{180} \pi = \frac{1}{2} \times 144 \times \frac{175}{180} \pi$

step 4

Simplifying the expression, we get $A = 72 \times \frac{175}{180} \pi = 35 \times \pi$

step 5

The area of the sector is therefore $35 \pi \text{ cm}^2$

C

Key Concept

Area of a Sector

Explanation

The area of a sector is calculated by the formula $A = \frac{1}{2} r^2 \theta$, where the angle $\theta$ must be in radians.

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