Question

H. Find the AREA of the circular sector shown in the following figure.

5 in
30-
(h
MacBook Bra

Answer 1

well, from the picture let's notice that its radius is 5 inches, so

`\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=5\\ \theta = 30 \end{cases}\implies \begin{array}{llll} A=\cfrac{(30)\pi (5)^2}{360}\implies A=\cfrac{25\pi }{12} \\\\\\ A\approx 6.54~in^2 \end{array}`

Answer 2

The circular sector's area, computed using the formula with the angle in radians, is 25π/6 square inches which is approximately 6.54 in².

To determine the area of a circular sector, we use the formula A = (1/2) r^2 θ, where r is the radius and θ is the central angle in radians. In this case, with a radius of 5 inches and θ = 30 degrees, it's important to convert degrees to radians.

The conversion involves multiplying the degree measure by π/180. For 30 degrees, this results in π/6 radians. Substituting this into the formula, we get:

A = (1/2) × (5)^2 × (π/6)

Solving this expression yields the area of the circular sector:

A = 25π/6

A ≈ 6.54 in²

Hence, the area of the circular sector with a 5-inch radius and a central angle of 30° is 6.54 square inches

In summary, applying the area formula with proper conversion of the angle to radians results in an area of 6.54 square inches for the given circular sector.