The diameter of a circle found by measurement 5.2 cms with a maximum error 0.05 cms. The maximum error in its area is
Answers
If the diameter of the circle is 5.2 cm with a maximum error of 0.05 cm then the maximum error in its area is 0.41 cm².
Step-by-step explanation:
The given diameter of the circle = [5.2 ± 0.05] cm
Here we will find the area of the circle in both the cases first one with error and another one without error to get the actual area and the calculated area respectively:
Step 1: Finding the actual area
The actual diameter = 5.2 – 0.05 = 5.15 cm
So, the actual radius = [actual diameter]/2 = 5.15/2 = 2.575 cm
∴ The actual area of the circle = πr² = (22/7) * 2.575² = 20.839 cm²
Step 2: Finding the calculated area
The calculated area of the circle = πr² = (22/7) * 2.6² = 21.245 cm²
Step 3:
Thus,
The maximum error in calculating the area of the circle is given by,
= [The calculated area] – [The actual area]
= [21.245 - 20.839 ] cm²
= 0.406 cm²
≈ 0.41 cm ²
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