Question

Consider a solid cylindrical object, like a soup can. Let a be the radius and let b be its height. Let V be its volume and let S be its total surface area (top and bottom included).
(a) When is V more sensitive to changes in a than to changes in b, and when is it more sensitive to changes in b than to changes in a?

Answer 1

So the Volume is pie a^2 b

And I believe I have to derive something but I don't really understand it.

Answer 2

Not sure what 'more sensitive to changes means'
Does it mean the derivative is higher?

Answer 3

Yeah, that's what I'm confused about the book doesn't have any problems similar to it that I can even compare it to.

Answer 4

1. Consider a solid cylindrical object, like a soup can. Let a be the radius and let b be its height.
Let V be its volume and let S be its total surface area (top and bottom included).
(a) When is V more sensitive to changes in a than to changes in b, and when is it more
sensitive to changes in b than to changes in a?
(b) Consider S in place of V and answer the same questions as in part (a)

2. The dimensions of a rectangular box are measured as 3,4 and 12 cm. If the
measurements may be in error by +-0.01, +-0.01 and +-0.03, respectively, calculate the length
of an interior diagonal and estimate the possible error in this leng

Answer 5

Just find both partial derivatives and compare them.

Answer 6

OKay, thank you!

Answer 7

best response