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Question
The trunk of a tree has a diameter of 30 cm. During the following year, the circumference grew 6 cm. What is the percentage increase in the area of the cross-section of the tree?
Solution
Area A = `pi"r"^2 = (pi"D"^2)/4`
dA = `(2pi"DdD")/4`
= `(pi"DdD")/2`
Percentage of increasing Area of the trees cross-section = `"dA"/"A" xx 100`
= `((pi"DdD")/2)/((pi"D"^2)/4) xx 100`
= `(2"dD")/"D" xx 100`
= `(2 xx 6/pi)/30 xx 100`
= `12/(30pi) xx 100`
= `40/pi`%
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