find the arc length of a sector if the radius is 5cm and the area of the sector is 74.5

Understand Relationship: Understand the relationship between the area of a sector and the arc length. The area of a sector (A) of a circle with radius (r) and central angle (θ) in radians is given by the formula A = (1/2) * r^2 * θ. To find the arc length (L), we use the formula L = r * θ. We need to find θ first to calculate L.Calculate Central Angle: Calculate the central angle (θ) using the area of the sector. We have the area of the sector (A = 74.5 cm²) and the radius (r = 5 cm). We can rearrange the area formula to solve for θ: A = (1/2) * r^2 * θ 74.5 = (1/2) * 5^2 * θ 74.5 = (1/2) * 25 * θ 74.5 = 12.5 * θ θ = 74.5 / 12.5 θ = 5.96 radians (approximately)Calculate Arc Length: Calculate the arc length (L) using the central angle (θ) and the radius (r). Now that we have θ, we can use the arc length formula: L = r * θ L = 5 cm * 5.96 radians L = 29.8 cm

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find the arc length of a sector if the radius is $5\,\text{cm}$ and the area of the sector is $74.5$

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Algebra 2

Find the radius or diameter of a circle

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Q. find the arc length of a sector if the radius is

5\,\text{cm}

and the area of the sector is

74.5

Understand Relationship: Understand the relationship between the area of a sector and the arc length. The area of a sector $A$ of a circle with radius $r$ and central angle $\theta$ in radians is given by the formula $A = \frac{1}{2} \times r^2 \times \theta$ . To find the arc length $L$ , we use the formula $L = r \times \theta$ . We need to find $\theta$ first to calculate $L$ .
Calculate Central Angle: Calculate the central angle ( $\theta$ ) using the area of the sector. $\newline$ We have the area of the sector ( $A = 74.5 \, \text{cm}^2$ ) and the radius ( $r = 5 \, \text{cm}$ ). We can rearrange the area formula to solve for $\theta$ : $\newline$ $A = (1/2) \cdot r^2 \cdot \theta$ $\newline$ $74.5 = (1/2) \cdot 5^2 \cdot \theta$ $\newline$ $74.5 = (1/2) \cdot 25 \cdot \theta$ $\newline$ $74.5 = 12.5 \cdot \theta$ $\newline$ $\theta = 74.5 / 12.5$ $\newline$ $\theta = 5.96$ radians (approximately)
Calculate Arc Length: Calculate the arc length $L$ using the central angle $\theta$ and the radius $r$ . Now that we have $\theta$ , we can use the arc length formula: $L = r \times \theta$ $L = 5 \, \text{cm} \times 5.96 \, \text{radians}$ $L = 29.8 \, \text{cm}$