1.

In a sphere the rate of change of surface area isA. 8π times the rate of change of diameterB. 2π times the rate of change of diameterC. 2π times the rate of change of radiusD. 8π times the rate of change of radius

Answer»

Correct answer is D.

The surface area of a sphere, with radius r, is defined as

A(r) = 4πr2 – (1)

Differentiating (1) with respect to t, we get

\(\frac{dA}{dt}=8\pi r\frac{dr}{dt}\)

= 8π×(current radius)×(rate of change of radius)



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