Q3 of 78 Page 13

Mark the correct alternative in the following:

The radius of a sphere is changing at the rate of 0.1 cm/sec. The rate of change of its surface area when the radius is 200 cm is


The surface area of a sphere, of radius r, is defined by

A(r)=4πr2 – (1)


Given that and r=200cm, we have to calculate


Differentiating (1) with respect to t, we get



Substituting values, we get


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If at what rate in cubic units is V increasing when


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Side of an equilateral triangle expands at the rate of 2 cm/sec. The rate of increase of its area when each side is 10 cm is


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A cone whose height is always equal to its diameter is increasing in volume at the rate of 40 cm3/sec. At what rate is the radius increasing when its circular base area is 1 m2?


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Mark the correct alternative in the following:

A cylindrical vessel of radius 0.5 m is filled with oil at the rate of 0.25π m3/minute. The rate at which the surface of the oil is rising, is