Respuesta :
Answer:
Step-by-step explanation:
area of circle=πr²
area of reqd. sector=πr²/4
(∵90/360=1/4)
reqd. area=π×3²/4=9π/4≈(9×3.14)/4≈7.065 square feet.
The area of a sector which is bounded by an arc of 90 degrees and the part of a circle which has a radius of 3 feet is 7.06 ft².
What is the area of a circular sector?
The area of the circular sector is the space occupied by the it.
The area of the circular sector is the half of the product of the angle of the sector and the square of the radius of the circle when the angle is measure in radian.
It can be given when angle is measured in degrees as,
[tex]A=\dfrac{\theta}{360}\times\pi r^2[/tex]
Here, (r) is the radius of the circle and θ is the angle of the sector.
A circle has a radius of 3 feet. A sector in this circle is bounded by an arc of 90 degrees. Thus, the area of this sector is,
[tex]A=\dfrac{90}{360}\times \pi (3)^2\\A=7.06\rm\;ft^2[/tex]
Hence, the area of a sector which is bounded by an arc of 90 degrees and the part of a circle which has a radius of 3 feet is 7.06 ft².
Learn more about the area of a circular sector here;
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