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Question
The edge of a cube is decreasing at the rate of`( 0.6"cm")/sec`. Find the rate at which its volume is decreasing, when the edge of the cube is 2 cm.
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Solution
Let x be the edge of the cube and V be its volume at any time t.
Then V = x3
Differentiating both sides w.r.t. t, we get
`"dV"/"dt" = 3x^2"dx"/"dt"`
Now, `dx/dt = (0.6"cm")/sec` and x = 2 cm
∴ `"dV"/dt` = 3(2)2(0.6)
= 7.2
Hence, the volume of the cube is decreasing at the rate of `(7.2"cm"^3)/sec`.
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