Video Transcript
The area of a circle is 160 square
centimeters and a central angle of a sector is 71 degrees. Find the area of the sector giving
the answer to two decimal places.
In this problem, we have a circle
whose area we know and a sector with a central angle of 71 degrees whose area we
wish to calculate. We recall that in order to
calculate the area of a sector with a central angle of 𝜃 degrees, we take the area
of the full circle, 𝜋𝑟 squared, and multiply it by the fraction of the circle that
our sector represents; that’s 𝜃 over 360.
In this problem though, we don’t
need to calculate the area of the circle using 𝜋𝑟 squared because we’ve been given
it. So, we can just substitute the
relevant information. 𝜃 is 71 degrees. So, we have 71 over 360 multiplied
by the area of the circle which is 160. We could evaluate this on our
calculators or we could first simplify by canceling a factor of 40 from the
numerator and denominator to give 71 over nine multiplied by four.
Now, we can evaluate and it gives
284 over nine or 31.5 recurring. Rounding to two decimal places and
our value is 31.56. And the units for this area will be
the same as the units for the area of the original circle; they’re square
centimeters. So by multiplying the area of the
circle by the fraction of the circle that this sector represents, we’ve found that
the area of the sector to two decimal places is 31.56 square centimeters.
