What is the area of a sector with a central angle of 3π/5 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.

Answer:the area of a sector to the nearest hundredths is, 105.84 cm^2Step-by-step explanation:Area of a sector(A) is given by:[tex]A = \frac{r^2}{2} \theta[/tex]          .....[1]where,r is the radius and[tex]\theta[/tex] is the angle in radian.As per the statement: a central angle of 3π/5 radians and a diameter of 21.2 cm⇒[tex]\theta = \frac{3 \pi}{5}[/tex] We know that:Diameter(d) = 2(radius(r))⇒[tex]21.2 = 2r[/tex]⇒[tex]10.6 = r[/tex]or r = 10.6 cmSubstitute these in [1] we have;[tex]A = \frac{10.6^2}{2} \cdot \frac{3 \pi}{5}[/tex]use 3.14 for π[tex]A = \frac{112.36}{2} \cdot \frac{3 \cdot 3.14}{5}[/tex]⇒[tex]A = 56.18 \cdot 1.884[/tex]Simplify:⇒[tex]A = 105.84312[/tex] square cmtherefore, the area of a sector to the nearest hundredths is, 105.84 cm^2