Question

An ice cube is melting such that the side of the cube is decreasing at the rate of 1/4 t^2 cm / min. It is given that the side of the cube is 8cm at the start of the experiment. Calculate the length of the side of the cube when t = 4? ( answer 2 2/3 cm)

Answer 1

ds/dt = -(1/4) t^2

s = -(1/12) t^3 + 8
when t = 4

s = - (1/12)(4*16) + 8
= -16/3 + 24/3
= 8/3
= 2 2/3