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Question

If the diagonal of a square is changing at the rate of 0.5cm/s.

Then, the rate of change of area, when the area is 400cm2, is


A

202cm2/s

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B

102cm2/s

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C

1102cm2/s

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D

102cm2/s

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E

52cm2/s

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Solution

The correct option is B

102cm2/s


Explanation for the correct option:

Step-1: Determine the rate of change on the side

Let the side length of the square is acm.

Thus, the length of the diagonal is s=a2cm.

Let the time denoted by t.

Differentiate both sides of the equation with respect to t.

dsdt=dadt2.

It is given that the rate of change in diagonal is dsdt=0.5cm/s.

Thus, dadt2=0.5cm/s

dadt=122cm/s

Step-2: Determine the rate of change in the area

The area of the square is A=a2.

Differentiate both sides of the equation with respect to t.

dAdt=2adadt.

Substitute dadt=122cm/s in the above equation.

dAdt=2a122dAdt=a2cm2/s

The given area is A=400cm2.

a2=20cm2a=20cm

Therefore, dAdt=202cm2/s

dAdt=202dAdt=10×22dAdt=102cm2/s

Therefore, the rate of change of area, when the area is 400cm2, is 102cm2/s.

Hence, option(B) i.e. 102cm2/s is the correct option.


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