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Find the approximate change in the volume V of acube of side x metres caused by increasing the side by 1%. |
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Answer» Given that `(dx)/x xx 100 = 1%` Let volume of cube be V. `:. V=x^(3)` `rArr (dV0/(dx) = 3x^(2)` ` rArr (dV)/V = (3*x^(2)dx)/V = (3x^(2)dx)/x^(3) = 3 * (dx)/x` ` rArr (dV)/V xx 100 = 3 * (dx)/x xx 100` ` rArr" Percentage increase in volume " 3 xx 1% = 3%` . |
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