Answer:
1.
the area of a sector to the nearest hundredths is,
2.
the area of a sector to the nearest hundredths is,
Step-by-step explanation:
Area of a sector(A) is given by:
.....[1]
where,
r is the radius and
is the angle in radian.
(1)
As per the statement:
a central angle of 5π/7 radians and a diameter of 5.6 in
⇒
We know that:
Diameter(d) = 2(radius(r))
⇒
⇒
or
r = 2.8 in.
Substitute these in [1] we have;
use 3.14 for π
⇒
Simplify:
⇒ square inches
therefore, the area of a sector to the nearest hundredths is,
Similarly:
2.
a central angle of 4π/5 radians and a radius of 11 cm
⇒
Substitute these in [1] we have;
use 3.14 for π
⇒
Simplify:
⇒ square inches
therefore, the area of a sector to the nearest hundredths is,