Find the area of a sector with a central angle of 190° and a diameter of 5.1 cm. Round to the nearest tenth.
Please Help I just don't get it
Fraction, not "fractions."
A few hints:
What is the area of a circle with a diameter of 5.1 cm?
What fractions of a whole circle is a 190° sector?
Isn't a circle a "sector" with a 360° central angle?
(190/360) (pi D^2/4)
To find the area of a sector, you can use the formula:
Area of sector = (θ/360) × πr²
Where:
- θ is the central angle (in degrees)
- r is the radius of the sector
In this case, we are given the central angle (θ = 190°) and the diameter (which is twice the radius). So, we need to find the radius (r) first.
Radius (r) = Diameter / 2 = 5.1 cm / 2 = 2.55 cm
Now, substitute the values of θ and r into the formula:
Area of sector = (190/360) × π(2.55)²
Calculating this expression:
Area of sector = (0.5278) × π(6.5025)
Area of sector ≈ 10.7943 cm² (rounded to four decimal places)
Rounding to the nearest tenth as requested, the area of the sector is approximately 10.8 cm².