Question

An amusement park has discovered that the brace that provides stability to the ferris

wheel has been damaged and needs work. The arc length of steel reinforcement that

must be replaced is between the two seats shown. The sector area is 28.25 square

feet and the radius is 12 feet.

Brace that provides


A: 4.708

B: 2.669

C: 9.417

D: 2.354

stability to the ride

What is the length of steel that must be replaced?

04.708 feet

Answer 1

Hence the correct answer is option (A) 4.708.

Explanation:

Solution:-

Now, we need to find the angle of the sector by using sector formula,

`A = 28.25 ft^(2) \\r = 12ft.\\\\28.25 = (\theta)/(360^(o) ) * \pi * 12^(2) \\\\\theta=(28.25* 360)/(12 *12 * \pi) \\\\\theta =( (70.625)/(\\pi) )^(o)`

We now convert the angle to radian

`\theta = (70.625)/(\pi) * (\pi)/(180)\\\\\theta = 0.39236 radian`

Now we calculate the length of arc by arc formula

`\theta=(I)/(12) \\\\0.39236 =(I)/(12)\\\\I = 4.708 feet.`

So, The length of steel that must be replaced is 4.708 ft.