# Thread: Ice Cube

1. ## Ice Cube

I have two problems that are just bugging me and can't figure out how to get the answers. So I am begging you guys to help me out with them.

A) A cube is melting a uniform rate of 3 in^2/hr. Fin the rate at which each side of the cube is decreasing when each side is 7in. Answer should be in in/min.

B) A cube of ice is melting at a rate of 2in^3/hr, find the rate at which the surface area is decreasing when the sides are 5inches. Answer should be in in^2/min.

Thanks for the help if you can.

2. A) A cube is melting a uniform rate of 3 in^2/hr. Fin the rate at which each side of the cube is decreasing when each side is 7in. Answer should be in in/min.
The volume of the cube is $V=x^{3}$

We are given $\frac{dV}{dt} = -3, \;\ x=7$

We need dx/dt.

Differentiate implicitly:

$\frac{dV}{dt}=3x^{2}\cdot\frac{dx}{dt}$

Plug in the knowns and solve for dx/dt.