1billionairehea
contestada

What is the area of a sector with a central angle of 3π5 radians and a diameter of 21.2 cm?

Use 3.14 for π and round your final answer to the nearest hundredth.

Enter your answer as a decimal in the box.


cm²

Respuesta :

calculista
we know that

Area of a circumference=π*r²
for diameter=21.2 cm---------> r=10.6 cm
A=π*10.6²--------> A=π*112.36 -------> A=352.81 cm²

if 2π radians (full circumference) has an area of -----------------> 352.81 cm²
 3π/5 radians-------------------------------------> X
X=[(3π/5)*(352.81)]/2π---------> X=105.84 cm²

the answer is 105.84 cm²

The area of the sector has a diameter of 21.2 cm and a central angle of 3π/5 radians is 105.90 square cm.

What is a circle?

It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

The central angle of 3π/5 radians and a diameter of 21.2 cm.

Then the area of the sector will be

[tex]\rm Area = \dfrac{\theta}{2\pi} *\dfrac{\pi}{4} d^2[/tex]

Then put the values, we have

[tex]\rm Area = \dfrac{\frac{3\pi}{5}}{2\pi} *\dfrac{\pi}{4} (21.2)^2\\\\\\\rm Area = \dfrac{3\pi}{10\pi} *\dfrac{3.14}{4} *449.44\\\\\\Area = \dfrac{3}{10} *\dfrac{3.14}{4} *449.44\\\\\\Area = 105.8968 \approx 105.90 \ cm^2[/tex]

The area of the sector has a diameter of 21.2 cm and a central angle of 3π/5 radians is 105.90 square cm.

More about the circle link is given below.

https://brainly.com/question/11833983

Otras preguntas