Question

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 1

Answer:

the area of a sector to the nearest hundredths is, 105.84 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.

As per the statement:

a central angle of 3π/5 radians and a diameter of 21.2 cm

⇒$\theta = \frac{3 \pi}{5}$

We know that:

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

⇒$21.2 = 2r$

⇒$10.6 = r$

or

r = 10.6 cm

Substitute these in [1] we have;

$A = \frac{10.6^2}{2} \cdot \frac{3 \pi}{5}$

use 3.14 for π

$A = \frac{112.36}{2} \cdot \frac{3 \cdot 3.14}{5}$

⇒$A = 56.18 \cdot 1.884$

Simplify:

⇒$A = 105.84312$ square cm

therefore, the area of a sector to the nearest hundredths is, 105.84 cm^2

Answer 2

answer: 105.84 cm^2

took the test and it was correct :)