Question

1)

Answer 1

1. 8.79 which becomes 8.80 after rounding. 
2. 152.05

Answer 2

Answer:

1.

the area of a sector to the nearest hundredths is, $8.79 in^2$

2.

the area of a sector to the nearest hundredths is, $151.98 cm^2$

Step-by-step explanation:

Area of a sector(A) is given by:

$A = \frac{r^2}{2} \theta$          .....[1]

where,

r is the radius and

$\theta$ is the angle in radian.

(1)

As per the statement:

a central angle of 5π/7 radians and a diameter of 5.6 in

⇒$\theta =\frac{5 \pi}{7}$

We know that:

Diameter(d) = 2(radius(r))

⇒$5.6 = 2r$

⇒$2.8 = r$

or

r = 2.8 in.

Substitute these in [1] we have;

$A = \frac{2.8^2}{2}\cdot \frac{5 \pi}{7}$

use 3.14 for π

$A = \frac{7.84}{2}\cdot \frac{5 \cdot 3.14}{7}$

⇒$A = 3.92 \cdot 2.24285714$

Simplify:

⇒$A =8.79199999$ square inches

therefore, the area of a sector to the nearest hundredths is, $8.79 in^2$

Similarly:

2.

a central angle of 4π/5 radians and a radius of 11 cm

⇒$\theta = \frac{4 \pi}{5}$

Substitute these in [1] we have;

$A = \frac{11^2}{2} \cdot \frac{4 \pi}{5}$

use 3.14 for π

$A = \frac{121}{2} \cdot \frac{4 \cdot 3.14}{5}$

⇒$A =60.5 \cdot 2.512$

Simplify:

⇒$A =151.976$ square inches

therefore, the area of a sector to the nearest hundredths is, $151.98 cm^2$