Question

What is the area of a sector with a central angle of 210 degrees and a diameter of 4.6 m? Round the answer to the nearest tenth.

Answer 1

theta (the angle)/360 X pie (r Squared)

Answer 2

..Uh.. I got an answer that wasn't one of my selections. I'm really confused, I'm sorry.

Answer 3

It is ok :D

Answer 4

Area of entire circle = PI * r²
Area of entire circle = PI * 4.6²
Area = PI * 21.16
Area = 66.476

Area of 210° sector =
66.476 * (210 / 360) = 66.476 * 0.5833333333
=38.777 sq meters

Answer 5

Wow, thanks!

Answer 6

You are welcome.
:-)

Answer 7

Uh, @wolf1728 the area is \(A=\pi r^2\) but we are given a diameter, not a radius, which means the answer computed is off by a factor of 4.

\[A_{circle} = \pi r^2 = \pi \frac{d^2}{4} = \pi\frac{4.6\text{ m}^2}{4} = 5.29\pi \text{ m}^2\]\[A_{sector} = A_{circle}(\frac{210^\circ}{360^\circ}) \approx 5.29\pi \text{ m}^2*\frac{7}{12} \approx 3.086\pi \text{ m}^2 \approx 9.694\text{ m}^2\]which rounded to the nearest tenth as requested is \(9.7\text{ m}^2\)

Answer 8

I imagine that 38.8 m^2 WAS one of the answer choices, with the intent of catching anyone who didn't read carefully enough...