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What is the length of a 30° - arc? if its area is 144πcm²

What is the length of a 90° - arc? if its area is 144πcm²

 Apr 14, 2023
edited by Guest  Apr 14, 2023
edited by Guest  Apr 14, 2023
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The length of an arc can be calculated using the formula:

Length of arc = (angle/360) * 2πr

where r is the radius of the circle.

(a) For a 30° - arc with an area of 144π cm², we first need to find the radius of the circle. The area of the full circle is πr², so the radius is:

πr² = 144π r² = 144 r = 12 cm

Now we can calculate the length of the 30° - arc:

Length of 30° - arc = (30/360) * 2π(12) = π/6 * 24 = 4π cm

Therefore, the length of the 30° - arc is 4π cm.

(b) For a 90° - arc with an area of 144π cm², we can use the same radius as before:

πr² = 144π r² = 144 r = 12 cm

Now we can calculate the length of the 90° - arc:

Length of 90° - arc = (90/360) * 2π(12) = π/2 * 12 = 6π cm

Therefore, the length of the 90° - arc is 6π cm.

 Apr 14, 2023

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