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) $144 \pi \mathrm{cm}^{2}$

Question

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) $144 \pi \mathrm{cm}^{2}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the area of a sector of a circle, we use the formula $A = \frac{1}{2} r^2 heta$ where $A$ is the area, $r$ is the radius, and $ heta$ is the central angle in radians. ‖ ‖ 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: $A = \frac{1}{2} imes 12^2 imes \frac{175}{180} \pi = \frac{1}{2} imes 144 imes \frac{175}{180} \pi$. ‖ ‖ step 4 ⋮ Simplifying the expression, we get $A = 72 imes \frac{175}{180} \pi = 35 imes \pi$. ‖ ‖ step 5 ⋮ The area of the sector is therefore $35 \pi ext{ cm}^2$. ‖ ***C*** ∻Key Concept∻ ⚹Area of a Sector⚹ ∻Explanation∻ ⚹The area of a sector is calculated by the formula $A = \frac{1}{2} r^2 heta$, where the angle $ heta$ must be in radians.⚹◊What is the formula to calculate the area of a sector given the central angle and radius?⍭ Generate me a similar question◊

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