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# Surface area Suppose that the radius rr and surface area S=4πr2S=4πr^{2} of a sphere are differentiable functions of tt. Write an equation that relates dS/dtdS/dt to dr/dtdr/dt.

Solid Geometry
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asked 2020-12-28
Surface area Suppose that the radius rr and surface area $$S=4πr2S=4πr^{2}$$
of a sphere are differentiable functions of tt. Write an equation that relates dS/dtdS/dt to dr/dtdr/dt.

## Answers (1)

2020-12-29

$$\frac{dS}{dt} = 8pir\frac{dr}{dt}$$ Knowing implicit differentiation and the given equation, we can take the derivative with respect to t. Doing this we get $$\frac{dS}{dt} = 8\pi r\frac{dr}{dt}$$. We get this by using implicit differentiation and going left to right throughout the problem.

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