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

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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°`

Page 2

We have 

`r=5 cm`

length of the arc(l)=3.5 cm

Now we will find the area of the sector. 

Area of the sector=`1/2xxlr`

Substituting the values we get, 

Area of the sector=`1/2xx3.5xx5`..........(1)

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

Area of the sectors=`1/2xx17.5`

Area of the sectors=`8.75`

Therefore, area of the sector is `8.75 cm^2`