A circle has a radius of 8cm. What is the area of the sector with a central angle of 80∘? 1289𝜋cm2 1618𝜋cm2 169𝜋cm2

Question

A circle has a radius of 8cm. What is the area of the sector with a central angle of 80°?

1289𝜋cm²
1618𝜋cm²
169𝜋cm²

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Solution

The area of a sector of a circle can be found using the formula:

Area of sector = (central angle/360) * π * r²

where:

the central angle is given as 80 degrees,
r is the radius of the circle, which is given as 8 cm.

Substituting these values into the formula gives:

Area of sector = (80/360) * π * 8²

Solving this gives:

Area of sector = (2/9) * π * 64

Area of sector = 128/9 * π cm²

So, the area of the sector with a central angle of 80 degrees is 128/9 * π cm². This is not exactly equal to any of the options given, but it is closest to 169𝜋cm².

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A circle has a radius of 8cm. What is the area of the sector with a central angle of 80∘? 1289𝜋cm2 1618𝜋cm2 169𝜋cm2

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