Question

What is the angle subtended at the centre of a circle of radius 6 cm by an arc of length 3 π cm?

Answer 1

We have 

`r=6cm`

length of the arc=`3pi cm`

We will find the angle subtended at the centre of a circle.

Length  of the arc=`θ/360xx2pi r`

Substituting the values we get,

3pi=`θ/360xx2pixx6 `    ............(1)

Now we will simplify the equation (1) as below,

   ` 3pi=θ/360xx2pixx6`..........(1) 

    `3pi=θ/30xxpi`

    `3=θ/30`

    `⇒ θ=90°`

Therefore, angle subtended at the centre of the circle is `90°`