Question

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Answer 1

12π m²

Explanation:

We are interested in calculating the area bounded by the given arcs .

we know that if
`\theta` is the angle subtended at the centre by the arc , then ; the area is given by ,

`\longrightarrow Area =(\theta)/(360^o)* \pi r^2 \\`

here we have ,

• 
  `\theta = 120^o`
• 
  `r = 6m`

Therefore on substituting the respective values, we have;

`\longrightarrow Area =(120^o)/(360^o)* \pi (6m)^2 \\`

Simplify,

`\longrightarrow Area =(1)/(3)* \pi * 36m^2 \\`

`\longrightarrow \underline{\underline{ Area = 12\pi \ m^2}} \\`

And we are done!

Answer 2

Answer: The result is 12π m²

Step-by-step explanation:

To solve, we must find the Area of the circle, for this we must do the following:

`\: \sf{Area} = \cfrac{ \sf{θ} }{360 {}^( \circ) } * \sf{\pi r {}^(2) }`

Once having the above, we must extract the results that we have to put in the fraction, where:

• 
  `\theta = 120 {}^( \circ)`
• 
  `\sf{r = 6m}`

Once we have the above, we must substitute the respective values...

`\sf Area = \cfrac{120 {}^( \circ) }{360 {}^( \circ) } * \pi(6m) {}^(2)`

Now to finish, let's simplify:

`\sf{Area = \cfrac{1}{3}* \pi * 36m {}^(2) }`

`\sf Area = 12 \pi \: m {}^(2)`

Rpt: The result is 12π m²