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  • If an edge of a variable cube is increasing at the rate of 0.5 cm/sec,at what rate is its surface area increasing when its edge is 12cm?

If an edge of a variable cube is increasing at the rate of 0.5 cm/sec,at what rate is its surface area increasing when its edge is 12cm?

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Let a cm be the side of a cube and S its surface area at any time t seconds, then S=6a2 .....(i) 
Differentiating w.r.t  t ,we get fracmathrmd smathrmd t=6.2afracmathrmd amathrmd t=12afracmathrmd amathrmd t     ..........(ii)

But fracmathrmd amathrmd t=0.5cm/sec =frac12cm/sec, (given)
herefore , From, (ii),fracmathrmd smathrmd t=12a imesfrac12=6a
When a=12cm, fracmathrmd smathrmd t=6 imes12=72
Hence the area is increasing at the rate of 72cm2 /sec

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Deependra Verma

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