Question

) As an ice cube melts its surface area is decreasing at a rate of 6cm2/sec. Find the rate at which the length of each side is decreasing at the moment when each side has length 2 cm. [Hint: a cube has 6 sides and each side has area x 2 where x is the side length]

Answer 1

Answer:

The rate of decreasing of the length is 0.25 cm/s.

Step-by-step explanation:

The surface area of the ice cube is:

$A_{ice}=6x^{2}$

Where x is the side of the cube.

Let's take the derivative of A with respect to "t" to get the rate of change.

$\frac{dA_{ice}}{dt}=12x\frac{dx}{dt}$

We know that dA/dt = 6 cm²/s and x is 2 cm, so we just need to solve it for dx/dt which is the rate change of the length.

$6=12(2)\frac{dx}{dt}$

$\frac{dx}{dt}=\frac{1}{4}\: cm/s$

Therefore, the rate of decreasing of the length is 0.25 cm/s.

I hope it helps you!