Question

At what rate is the diagonal of a cube increasing if its edges are increasing at a rate of 2 cm/s?

Answer 1

the diagonal of a cube =
\[d = \sqrt{3x^2}=\sqrt{3}x\]
so the length of the diagonal of a cube is proportional to the lenght of the side and therefore they will change at the same rate

Answer 2

i got dz/dt = 2√3

Answer 3

2* radical 3

Answer 4

oh sorry, yes of course it wil be
\(\sqrt{3} \times\) times the rate the edges change
You're right