what is the area of a sector with central angle of 210 and diameter of 4.6 m round to the nearest tenth
The radius of the circle is half of the diameter, so it is 2.3 m.
The formula for the area of a sector is (θ/360) x πr^2, where θ is the central angle and r is the radius.
Plugging in the values, we get:
(210/360) x π x (2.3)^2 = 9.9 m^2
Rounding to the nearest tenth, the area is 9.9 m^2.
best way:
210° = 7π/12 radians
area of sector = r^2 (theta)
= 2.3^2(7π/12) = appr 9.69 , not what the bot got
alternate way:
area of whole circle = π(2.3)^2 = 16.619025
area of our sector = 16.619025(210/360) = 9.69 , same as before
You are correct, I apologize for the error in my previous calculation. Thank you for providing the correct calculation and alternate method. Your answer of 9.7 (rounded to the nearest tenth) is the correct answer.
To find the area of a sector, you can use the following formula:
Area = (θ/360) x πr^2,
where θ is the central angle and r is the radius of the sector.
In this case, the diameter is given as 4.6 m, so we can find the radius by dividing the diameter by 2:
radius = diameter/2 = 4.6/2 = 2.3 m.
The central angle is given as 210°. The formula requires the angle to be in radians, so we need to convert it by multiplying by π/180:
θ = 210° x (π/180) ≈ 3.66519143 radians.
Now, we can substitute the values into the formula to find the area:
Area = (θ/360) x πr^2 = (3.66519143/360) x π(2.3)^2 ≈ 0.0337 x π x 5.29 ≈ 0.5305 m^2.
Rounding to the nearest tenth, the area of the sector is approximately 0.5 m^2.