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Find the area of the sector

Find the area of the sector-example-1

2 Answers

3 votes

Answer:

The easiest way to do this is to calculate the Area of the whole circle and then subtract the 1/4 of the missing piece.

So:

  • A=pi×81
  • and then pi×81/4
  • and then pi×81-[pi×81/4]
User Kuyabiye
by
8.5k points
2 votes

Answer:


\boxed {\boxed {\sf a \approx 190.9 \ yd^2}}

Explanation:

There are 2 formulas for the area of a sector, but since we are given the central angle in degrees (not radians), we will use this formula:


a= \frac {\theta}{360} * \pi r^2

Where θ is the central angle and r is the radius.

For this circle, the radius is 9 yards and the central angle is 270 degrees. We can substitute these values into the formula.


a= \frac {270}{360} * \pi * (9 \ yd )^2

Solve the fraction.


a=0.75 * \pi * (9 \ yd)^2

Solve the exponent.

  • (9 yd)²= 9 yd* 9 yd=81 yd²


a= 0.75 * \pi * 81 \ yd^2

Multiply all three numbers together.


a= 190.851753706 \ yd^2

The question asks us to round to the nearest tenth.

  • 190.851753706

The 5 in the hundredth place tells us to round the 8 up to a 9.


a \approx 190.9 \ yd^2

The area of the sector is approximately 190.9 square yards.

User Eric Svitok
by
8.3k points

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