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The volume of a cube is increasing at the rate of 18 cm 3 per second. When the edge of the cube is 12 c m, then the rate in c m 2 / s at which the surface area of the cube increases, is

Correct answer

6

Step-by-step solution

Let, x be the length of an edge, V be the volume and S be the surface area of the cube. d V d t = 18 , V = x 3 ⇒ d V d t = 18 = 3 x 2 d x d t ⇒ d x d t = 6 x 2 ⋯ i S = 6 x 2 ⇒ d S d t = 12 x d x d t … From i ⇒ d S d t = 12 x 6 x 2 ⇒ d S d t = 12 × 6 x = 6 ∵ Given x = 12 ∴ d S d t = 6 cm 2 /sec

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