The side of a square sheet is increasing at the rate of 4 cm per minute. At what rate is the area increasing when the side is 8 cm long?

Asked by Aaryan | 1 year ago |  56

##### Solution :-

Given the side of a square sheet is increasing at the rate of 4 cm per minute.

To find rate of area increasing when the side is 8 cm long

Let the side of the given square sheet be x cm at any instant time.

Then according to the given question, we can write as

The rate of side of the sheet increasing is, $$\dfrac{dx}{dt}$$ = 4cm/min ...(i)

Now the area of the square sheet at any time t will be  A = x2cm2

By applying derivative with respect to time on both sides

$$\dfrac{dA}{dt}$$ = $$2x\times 4 = 8x$$............(ii)

From the equation (i)

Therefore when the side is 8cm long,

the rate of area increasing will become  $$\dfrac{dA}{dt}$$ = 8 x 8 (from the equation (ii))

$$\dfrac{dA}{dt}$$= 64cm2/min

Thus the area is increasing at the rate of 64cm2/min when the side is 8cm long.

Answered by Sakshi | 1 year ago

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