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in a circle with a radius of 7 feet, the radian measure of the central angle subtended by an arc with a length of 4 feet is 0.57 . the area of the sector formed by the arc is square feet. assume π

Sagot :

The area of the sector formed by the arc of the circle is 14 square feet.

What is sector of the circle?

A sector of a circle is a pie-shaped section of a circle formed by the arc and its two radii. A sector is formed when a portion of the circle's circumference (as well known as an arc) and two radii cross paths at both endpoints of a arc. A sector of a circle has the shape of a pizza slice or even a pie.

  • Two radii and an arc encircle a portion of a circle.
  • A circle is divided into two segments which are referred to as minor sectors as well as major sectors.
  • The major sector is represented by the larger portion of the circle, while the minor sector is represented by the smaller portion.

Now, according to the question;

Length of a sector is estimated by the formula = ∅×r

where ∅ is the angle formed by sector in radians and r is the radius of the circle.

Thus,

∅ = Length of a sector/r

The radius is r = 7 ft

The value of length of a sector = 4 ft

∅ = 4/7

∅ = 0.57 radians

Now, estimate the area of the sector.

area of a sector = (∅/2)×r²

Substituting the values.

area of a sector = (4/7/2)×7²

                          = (4/14)×49

area of a sector = 14 ft²

Therefore, the area of the sector is calculated as 14  ft².

To know more about the sector of the circle, here

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The complete question is-

In a circle with a radius of 7 feet, the radian measure of the central angle subtended by an arc with a length of 4 feet is . The area of the sector formed by the arc is square feet. Assume π = 3.14, and round your answers to the nearest hundredth.

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