Question

what is the area of a sector with central angle of 210 and diameter of 4.6 m round to the nearest tenth

Answer 1

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

Answer 2

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.

Answer 3

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.