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

The required length is 37.68 cm

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

Answer 2

The arc length of a circle is, 2.355 cm

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 = (\pi)/(4)`

Substitute the given values in [1] we have;

Use
`\pi = 3.14`

`l = 3 \cdot (\pi)/(4)= 3 \cdot (3.14)/(4) = 2.355` cm

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