find the angle of a sector of a circle of radius 35cm is 288' find the perimeter of the sector
Try that again so it makes sense.
To find the angle of a sector of a circle, you need to convert the given arc length into degrees.
Given:
Radius of the sector (r) = 35 cm
Arc length (l) = 288'
Formula to find the angle (θ) of a sector given the arc length is:
θ = (l / r) * (180 / π)
θ = (288' / 35) * (180 / π)
θ ≈ 134.57 degrees (rounded to two decimal places)
To find the perimeter of the sector, you need to find the length of the curved part of the sector (circumference) and add it to the length of the two radii.
Formula to find the perimeter (P) of a sector given the radius (r) and the angle (θ) is:
P = 2r + (r * θ * π / 180)
P = 2(35) + (35 * 134.57 * π / 180)
P ≈ 121.36 cm (rounded to two decimal places)
Therefore, the perimeter of the sector is approximately 121.36 cm.
To find the angle of a sector of a circle, you need to know the measure of the angle in degrees or in minutes, seconds (') notation. In this case, you have the angle measure in minutes.
To convert minutes (') to degrees, you need to divide the given number by 60. Therefore, 288' can be converted to degrees as follows:
288' ÷ 60 = 4.8 degrees
Now that you have the angle measure of the sector in degrees (4.8 degrees) and the radius of the circle (35 cm), you can calculate the perimeter of the sector.
The perimeter of a sector is given by the formula:
Perimeter = (angle/360) × (2π × radius)
Substituting the given values into the formula:
Perimeter = (4.8/360) × (2π × 35 cm)
Perimeter = (0.0133) × (2π × 35 cm)
Perimeter = 0.0133 × 70π cm
Perimeter = approximately 2.1965π cm or approximately 6.9033 cm (rounded to four decimal places)
Hence, the perimeter of the sector is approximately 2.1965π cm or approximately 6.9033 cm.