Question

Find the rate of change of the total surface area of a cylinder of radius r and height h, when the radius varies

Answer 1

Given that,

Radius = r

Height = h

We know that,

The total surface area of a cylinder is

$s=2\pi r^2+2\pi r h$

Where, r = radius

h = height

We need to calculate the rate of change of the total surface area of a cylinder

Using formula of surface area of a cylinder

$s=2\pi r^2+2\pi r h$

On differentiating

$\dfrac{ds}{dr}=4\pi r+2\pi h$

$\dfrac{ds}{dr}=2\pi(2r+h)$

Hence, The rate of change of the total surface area of a cylinder is $2\pi(2r+h)$

Answer 2

Answer:

Given that,

Radius = r

Height = h

We know that,

The total surface area of a cylinder is

$s=2\pi r^2+2\pi r h$

Where,

r = radius

h = height

We need to calculate the rate of change of the total surface area of a cylinder

Using formula of surface area of a cylinder

$s=2\pi r^2+2\pi r h$

On differentiating

$\dfrac{ds}{dr}=4\pi r+2\pi h$

$\dfrac{ds}{dr}=2\pi(2r+h)$

Hence, The rate of change of the total surface area of a cylinder is $2\pi(2r+h)$

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