# calculus

posted by .

The volume of a melting cube is decreasing at a rate of 10cm^3/min. How fast is the surface area of the ice cube decreasing when the length of an edge is 30 cm?

• calculus -

V = x^3
dV/dt = 3x^2 dx/dt
10 = 3x^2 dx/dt
dx/dt = 10/(3x^2)

SA = 6x^2
d(SA)/dt = 12x dx/dt
dx/dt = d(SA)/dt / (12x)

d(SA)d/t / (12x) = 10/(3x^2)
d(SA)/dt = 120x/(3x^2)
which when x = 30
= 120(30)/2700 = 4/3 cm/min

• calculus -

Thank you so much that was so helpful.

## Similar Questions

1. ### calculus

An ice cube is melting so that its edge length x is decreasing at the rate of 0.1 meters per second. How fast is the volume decreasing when x = 2 meters?

An ice cube that is 3 cm on each side is melting at a rate of 2 cm cubed per minute. how fast is the length of the side decreasing?
3. ### Calculus

If the volume of a cube is increasing at 24 in^3/min and the surface area of the cube is increasing at 12 in^2/min, what is the length of each edge of the cube?
4. ### Calculus

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 = …
5. ### calculus

An ice cube is melting, and the lengths of its sides are decreasing at a rate of 0.4 millimeters per minute. At what rate is the volume of the ice cube decreasing when the lengths of the sides of the cube are equal to 15 millimeters?
6. ### Calculus

The volume of an ice cube as it melts is given by the equation: V = 2.1x10^-5 t^3 - 6.5x10^-4 t^2 - 0.346 t + 21.31 Determine the rate at which the sides of the ice cube melt at both 10 and 75 minutes after the beginning of the melting …
7. ### math

an ice cube that is 8 cm on each side is melting at a rate of 4 cm^3 per min. how fast is the length of the side decreasing?
8. ### calculus

The edge of a cube office is decreasing at a constant rate of two cm per seconds .find the rate of change of its volume at that instant when the volume is 64m cube
9. ### Calculus

As an ice cube melts its surface area in decreasing at a rate of 6 cm^2 / sec. Find the rate at which the length of each side is decreasing at the moment when each side has length 2 cm.
10. ### Math calculus

An ice cube is 3 by 3 by 3 inches is melting in such a way that the length of one of its side is decreasing at a rate of half an inch per minute. Find the rate at which its surface area is decreasing at the moment when the volume of …

More Similar Questions