area of a sector of a circle of radius 36 cm is 54 pie cm square . find the length of the corresponding arc of the sector
9.43 cm
To find the length of the corresponding arc of the sector, we need to use the formula:
Arc Length = (θ/360) * 2πr
Where:
- θ is the central angle of the sector in degrees,
- r is the radius of the circle, and
- π is the mathematical constant approximately equal to 3.14159.
Given that the area of the sector is 54π cm², we can find the central angle (θ) using the formula for the area of a sector:
Area of Sector = (θ/360) * πr²
54π = (θ/360) * π(36)²
Divide both sides of the equation by π to simplify:
54 = (θ/360) * 36²
54 = (θ/360) * 1296
Multiply both sides of the equation by 360:
360 * 54 = 1296θ
19440 = 1296θ
Divide both sides of the equation by 1296:
θ = 19440 / 1296
θ ≈ 15
Now that we have the value of θ (central angle), we can substitute it into the formula for arc length:
Arc Length = (θ/360) * 2πr
Arc Length = (15/360) * 2π(36)
Simplify:
Arc Length = (1/24) * 2π(36)
Arc Length = (1/12) * π(36)
Arc Length = (1/12) * 36π
Arc Length = 3π cm
Therefore, the length of the corresponding arc of the sector is 3π cm.
i need the answer
can you not look up the formulas?
a = 1/2 r^2 θ, so
1/2 (36^2) θ = 54 pi (not pie!)
θ = 108π/1296 = 0.2618
now for the arc length,
s = rθ = 36 * 0.2618 = 9.42