1)What is the area of a sector with a central angle of 5π/7 radians and a diameter of 5.6 in.?Use 3.14 for π and round your final answer to the nearest hundredth.Enter your answer as a decimal in the box.2) What is the area of a sector with a central angle of 4π/5 radians and a radius of 11 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:1.the area of a sector to the nearest hundredths is, [tex]8.79 in^2[/tex]2.the area of a sector to the nearest hundredths is, [tex]151.98 cm^2[/tex]Step-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.(1)As per the statement: a central angle of 5π/7 radians and a diameter of 5.6 in⇒[tex]\theta =\frac{5 \pi}{7}[/tex] We know that:Diameter(d) = 2(radius(r))⇒[tex]5.6 = 2r[/tex]⇒[tex]2.8 = r[/tex]or r = 2.8 in.Substitute these in [1] we have;[tex]A = \frac{2.8^2}{2}\cdot \frac{5 \pi}{7}[/tex]use 3.14 for π[tex]A = \frac{7.84}{2}\cdot \frac{5 \cdot 3.14}{7}[/tex]⇒[tex]A = 3.92 \cdot 2.24285714[/tex]Simplify:⇒[tex]A =8.79199999[/tex] square inchestherefore, the area of a sector to the nearest hundredths is, [tex]8.79 in^2[/tex]Similarly:2.a central angle of 4π/5 radians and a radius of 11 cm⇒[tex]\theta = \frac{4 \pi}{5}[/tex] Substitute these in [1] we have;[tex]A = \frac{11^2}{2} \cdot \frac{4 \pi}{5}[/tex]use 3.14 for π[tex]A = \frac{121}{2} \cdot \frac{4 \cdot 3.14}{5}[/tex]⇒[tex]A =60.5 \cdot 2.512[/tex]Simplify:⇒[tex]A =151.976[/tex] square inchestherefore, the area of a sector to the nearest hundredths is, [tex]151.98 cm^2[/tex]