Question

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

Answer 1

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