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: 105.84 cm^2

took the test and it was correct :)

Answer 2

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

Explanation:

Area of a sector(A) is given by:

`A = (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 = (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 = (10.6^2)/(2) \cdot (3 \pi)/(5)`

use 3.14 for π

`A = (112.36)/(2) \cdot (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