Question

the volume of a cylinder is V = π r2 h

Answer 1

Answer:

Explanation:

We can write that in "multi variable" form as

f(r,h) = π r2 h

 

For the partial derivative with respect to r we hold h constant, and r changes:

Cylinder with r changing

f’r = π (2r) h = 2πrh

(The derivative of r2 with respect to r is 2r, and π and h are constants)

It says "as only the radius changes (by the tiniest amount), the volume changes by 2πrh"

It is like we add a skin with a circle's circumference (2πr) and a height of h.

 

For the partial derivative with respect to h we hold r constant:

Cylinder with r changing

f’h = π r2 (1)= πr2

(π and r2 are constants, and the derivative of h with respect to h is 1)

It says "as only the height changes (by the tiniest amount), the volume changes by πr2"

It is like we add the thinnest disk on top with a circle's area of πr2.

Answer 2

Explanation:

yes, volume of cylinder=πr^2h