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एक वृत्त की त्रिज्या r = 6 cm पर r के सापेक्ष क्षेत्रफल में परिवर्तन की दर (cm2/cm में) है

(A) 10 π

(B) 12 π

(C) 8 π

(D) 11 π

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सही विकल्प है (B) \(12 \pi\)

त्रिज्या r वाले वृत्त का क्षेत्रफल (A) है, \(A = \pi r^2\)

इस प्रकार त्रिज्या के साथ वृत्त के क्षेत्रफल में परिवर्तन की दर है

\(\Rightarrow \frac {dA}{dr} = 2 \pi r\)

\(r = 6 \text { cm}\)

\( \frac {dA}{dr} = 12 \pi \text{ cm}\)

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