Fred and circles

Geometry Level 2

Fred has a circle shaped farm, and water around it. His farm's area is 15239.5238858 c m 2 cm^2 . He has some special crops that only can grow if their dirt is DIRECTLY touching the water. If the water can only water the edge dirt and if the crops take 1cm space, how many crops can Fred plant on his farm.(crop = the special crop). Pi will be 3.14 for this challenge. NOTE: You can't place decimal crops. (For example 3.5 crops) Note2: round the radius to 3 decimal digits(3.6425 = 3.642, 6.4112 = 6.411)


The answer is 437.

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1 solution

Filip Jerleković
Jul 25, 2019

The formulas used are:

A = π r 2 A = \pi r^2 a.k.a. the area

and

C = 2 π r C = 2\pi r a.k.a. the circumference

(P.S: the order of multiplication in upper formulas is irrelevant)

So if the area is 15239.5238858 (marked as A), also pi is only 3.14.

This is how we get the radius out of the area:

A 3.14 \sqrt{\frac{A}{3.14}}

= 15239.5238858 3.14 = \sqrt{\frac{15239.5238858}{3.14}}

= 4853.35155599 = \sqrt{4853.35155599} = 69.6659999999 = 69.6659999999

if we round that to 3 digits, because the 4th digit is 9, we get 69.666.

Now we need to calculate the circumference of a circle whit radius of 69.666

Which, if we remove the decimal places is the answer!

So, this is the formula:

C = 2 π r C = 2\pi r

which in our case is:

C = 2 × 3.14 × 69.666 C = 2 \times 3.14 \times 69.666

which computed is:

437.50248

If we remove the decimals (because we can't have decimal crops), we get: 437 , which is the final answer

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