Question
Download Solution PDFएक परिवर्तनीय घन का किनारा 4 सेमी/सेकेंड की दर से बढ़ता है। जब किनारा 20 सेमी लंबा होता है, तो घन का आयतन कितनी तेजी से बढ़ता है?
Answer (Detailed Solution Below)
Detailed Solution
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दिया गया है कि घन का किनारा (L) दर = \(\rm{dL\over dt}\)= 4 सेमी/सेकेंड से बढ़ता है।
घन का आयतन V = L3
आयतन के वृद्धि की दर V =\(\rm{dV\over dt}\)= \(\rm{dV\over dL}×{dL\over dt}\)
\(\rm{dV\over dt}\) = \(\rm{d\over dL}\left[L^3\right]× {dL\over dt}\)
\(\rm{dV\over dt}\) = \(\rm 3L^2 × 4\) = 12L2
चूँकि L = 20 सेमी है।
\(\rm{dV\over dt}\) = 12 × 202
\(\rm{dV\over dt}\) = 12 × 400 = 4800 सेमी3/सेकेंड
Last updated on Jul 11, 2025
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