If the surface area of a cube is increasing at a rate of 3 . 6 c m 2 / s e c , retaining its shape; then the rate of change of its volume (in c m 3 / s e c ), when the length of a side of the cube is

Question

If the surface area of a cube is increasing at a rate of 3 . 6 c m 2 / s e c , retaining its shape; then the rate of change of its volume (in c m 3 / s e c ), when the length of a side of the cube is 10 c m , is:

TestHub · Accepted Answer

Surface area of cube s = 6 a 2 ⇒ d s d t = 12 a d a d t = 3 . 6 ⇒ 12 10 d a d t = 3 . 6 ⇒ d a d t = 0 . 03 c m / s e c Now, volume of cube V = a 3 ⇒ d v d t = 3 a 2 . d a d t = 3 ( 10 ) 2 0 . 03 = 9 c m 3 / s e c

Mathematics - Application of Derivative Question with Solution | TestHub

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