A wire is used to form a circular fence of radius 84 cm which is then later converted into a square-shaped fence by using the same length of wire. Find the ratio of the area of the circular region to the area of the square region?
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A wire is used to form a circular fence of radius 84 cm which is then later converted into a square-shaped fence by using the same length of wire. Find the ratio of the area of the circular region to the area of the square region?
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Answer:
11 : 14
Step-by-step explanation:
Radius of circular fence = 84cm
Toal Length of Wire = Circumference of circle = 2πR = 2×22/7×84 7 cancels 84 and 84 becomes 12 so the circumference of the circle is
2×22×12 = 528 cm
and the area of the circle will be πR² so it becomes :22/7×84×84 7 cancels one of the 84 and 84 becomes 12. so the area of the circle is 12×22×84 = 22176 cm²
if the wire is converted into a square the each side will be equal,and a square has 4 sides meaning that 1/4th of the total length of the wire would be 1 side of the square
so each side = 528/4 = 132 cm
and the area of the square will be S×S = 132×132 = 17424 cm²
the ratio of the area of circle : square is
22176 cm² : 17424 cm²
if we divide both by 144, we get : 121 : 154
if we divide those by 11 we get : 11 : 14