Calculus Rates of Change

Question

A large block of ice in the shape of a cube is melting. All sides, x, of the cube melt at the same rate. At what rate is the volume of the block decreasing when x=7 if its surface area is decreasing at a rate of 5 ft²/hr ?

Answer 1

SA(x) = 6x²

dSA/dt = 12x·dx/dt = 5

dx/dt = 5/84 ft/hr

V(x) = x³

dV/dt = 3x²·dx/dt = 3·49·5/84 = 35/4 ft³/hr