Question

The surface area of the ice cube is decreasing at the rate of 10cm^2/sec. At what rate the volume of the cube is changing when the area is 14cm^2?

Please explain thoroughly I have a test in 2 hours!

Answer 1

you need a formula relating the surface area of a cube to the volume

Answer 2

that is the only hard part
a quick calculation gives \[S=6\sqrt[3]{V}^2\] or better for calculus
\[\huge S=6V^{\frac{2}{3}}\]

Answer 3

that makes
\[S'=4V^{-\frac{1}{3}}V'\] plug in the numbers, solve for \(V'\)

Answer 4

Sorry was watching Israel PM speech! Thanks for the help