Ahmed MS wrote:A thin piece of 40 m wire is cut in two. One piece is a circle with radius of r. Other is a square. No wire is left over. Which represents total area of circle and square in terms of r?
a. Î r2
b. Î r2 + 10
c. Πr2 + ¼ π2r2
d. Î r2 + (40 - 2Ï€r)2
e. Πr2 + (10 - ½ Πr)2
The answer is E. Can anyone explain how?
Cheers!
Each answer choice includes πr², the area of the circle.
Eliminate A, which clearly does not include the area of the square.
Since πr² is included in each answer choice, we can ignore the first part of each remaining answer choice.
Our only concern is the second part:
the area of the square.
Plug in r = 4.
Circumference of circle = 2πr = 2π*4 ≈ 24.
Perimeter of square = remaining wire = 40-24 = 16.
Side of square = 16/4 = 4.
Area of square = 4² = 16.
Now we plug r=4 into the second part of each answer choice to see which yields our target of 16.
Only answer choice
E works:
(10 - ½ Πr)²
= (10 - ½ *3*4)²
= 4²
= 16.
The correct answer is
E.
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