How do I complete this problem on arc length?

a)  Length of the arc:    or  ≈ 26.18

b)  Area of the sector:     or  ≈ 65.45

c)  16 rad  or  2880°

Step-by-step explanation:

If a is the length of the arc, r is the radius of the sector and 0 the central angle in radians.

Use the formula:

                                                  [set r = 5 m, 0 = (given)]

·

⇒

⇒  ≈

The arc length of the watered sector is or ≈ 26.18.

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Recall, the area A of a circle (obviously ) with a radius is given by the formula:

So the area of the circular sector with radius r and central 0 (in radians) will be:

                                                         [set r = 5m , 0 = (given)]

⇒

⇒ =

⇒ = ≈ 65.45

The area of the watered sector is or ≈ 65.45 .

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From the given information we know that the sprinkler perform a full revolution (2 rad) every 15 sec so we will make the following proportion:

=                                            

⇒ =

⇒ 0 =

⇒ 0 =

⇒ 0 =

We can convert the angle of 0 = rad to degrees as shown:

= 16 ×

⇒ = 2880°

Finally the sprinkler rotates  16 rad  or  2880°  in 2 minutes.

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Step-by-step explanation: