Question

Use the fact that the length of an arc intercepted by an angle is proportional to the radius to find the arc length given that r = 3.0 cm and Θ = π4

Answer 1

Answer:

The arc length of a circle is, 2.355 cm

Step-by-step explanation:

Use the fact  that the length of an arc intercepted by an angle is proportional to the radius.

Let l be the length of an arc and r be the radius of the circle.

then;

$l \propto r$

then;

$l = r \theta$           .....[1]

It is also given: r = 3 cm and $\theta = \frac{\pi}{4}$

Substitute the given values in [1] we have;

Use $\pi = 3.14$

$l = 3 \cdot \frac{\pi}{4}= 3 \cdot \frac{3.14}{4} = 2.355$ cm

Therefore, the arc length of a circle is, 2.355 cm

Answer 2

Answer:

The required length is 37.68 cm

Step-by-step explanation:

We have given the radius of  which is 3 cm and  $\theta$which is $\pi\cdot 4$

We will use $\pi=3.14$

We know the formula for length of arc which is:

length of arc=radius x angle

We will substitute the values given we will get:

$length=3(3.14)(4)$

$length=37.68$

Hence, the required length is 37.68 cm