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QuestionFind the diameter of a merry-go-round with an area of 78.5 sq ft. Use π≈3.14\pi \approx 3.14 and round to the nearest hundredth.

Studdy Solution

STEP 1

Assumptions1. The area of the circular platform is78.5 square feet. We are using3.14 as the value of π\pi
3. The formula for the area of a circle is Area = \pi r^, where r is the radius of the circle4. The diameter of a circle is twice the radius, iameter=riameter =r

STEP 2

First, we need to find the radius of the circle. We can do this by rearranging the formula for the area of a circle to solve for r.
r=Areaπr = \sqrt{\frac{Area}{\pi}}

STEP 3

Now, plug in the given values for the area and π\pi to calculate the radius.
r=78.53.14r = \sqrt{\frac{78.5}{3.14}}

STEP 4

Calculate the radius.
r=78.3.14=r = \sqrt{\frac{78.}{3.14}} =

STEP 5

Now that we have the radius, we can find the diameter of the circle. This is done by multiplying the radius by2.
iameter=2riameter =2r

STEP 6

Plug in the value for the radius to calculate the diameter.
iameter=2times5iameter =2 \\times5

STEP 7

Calculate the diameter.
iameter=2times5=10iameter =2 \\times5 =10The diameter of the circular platform is10 feet.

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