Answer:
The perimeter of the quarter-circle is 200 cm.
Step-by-step explanation:
Given that the angle of quarter-circle is 90°. So using Length of Arc formula, you are able to find the length of curve :
[tex]arc = \frac{θ}{360} \times 2 \: \pi \: r[/tex]
Let r be radius = 56 cm,
Let θ = 90°
[tex]arc = \frac{90}{360} \times 2 \times\pi \times 56[/tex]
[tex] = \frac{1}{4} \times 2 \times \pi \times 56[/tex]
[tex] = \frac{1}{2} \times \pi \times 56[/tex]
[tex] = 28\pi \: cm[/tex]
We have already found the arc. Next we have to add up together to find the perimeter :
[tex]p = 56 + 56 + 28\pi[/tex]
[tex]p = 112 + 28\pi[/tex]
[tex]p = 200 \: cm \: (3s.f)[/tex]
