Question

The perimeter (210cm) of each sector has been given.

calculate x
give your answers to one dp.

Answer 1

we calculate the radius

210 =2*π*r

r= 210/(2*π) ≈ 33.4cm

calculation formula: (2*π*r*a)/360

with r the radius of the circle and α the angle of the angular sector expressed in degrees

The length of the arc of a circle with radius 33.4 and angle 30° is equal to

(2*π*33.4*30)/360≈17.479...≈17.48cm for π=3.14

Explanation:

Answer 2

Hello!

Answer:

`\Large \boxed{\sf x \approx 17.6cm}`

Explanation:

→ We want the value of
`\sf x`.

→ We know:

- The angle of this arc lenght is 30°

- The perimeter of the circle is 210cm

→ Calculate the radius:

We have this formula:

`\sf P =2\pi r`

Where:

- P is the perimeter of the circle

- r is the radius

→ We know that the perimeter of our circle is 210cm.

→ Let's replace P by 210:

`\sf 210 =2\pi r`

→ So we have this equation:

`\sf 210 = 2\pi r`

→ Let's solve r in this equation to find the radius:

◼ Divide both sides by 2:

`\sf (210)/(2) = (2\pi r )/(2)`

◼ Simplify both sides:

`\sf 105 =\pi r`

◼ Divide both sides by π:

`\sf (105)/(\pi) =(\pi r)/(\pi)`

◼ Simplify both sides:

`\sf r \approx 33.4`

→ So the radius of our figure is 33.4cm.

→ To calculate the lenght of the arc of the circle (x), we have this formula:

`\sf L= (2\pi ra)/(360)`

Where:

- L is the lenght of the arc of the circle

- r is the radius of the circle

- a is the value of the angle of the arc of the circle

→ Let's replace r by 33.4 and a by 30:

`\sf L= (2*\pi *33.4*30)/(360)`

→ Let's simplify the right side to find the lenght of the arc of the circle:

`\sf L= (2004\pi)/(360)`

`\sf L \approx 5.6\pi`

`\boxed{\sf L \approx 17.6}`

Therefore, the value of x is 17.6cm.

Have a nice day ;)