# A perfect cube shaped ice cube melts so that the length of its sides are decreasing at a rate of 2 mm/sec. Assume that the block retains its cube shape as it melts. At what rate is the volume of the ice cube changing when the sides are 2 mm each?

The volume is decreasing at a rate of

From simple differentiation, we know that

Therefore,

By signing up, you agree to our Terms of Service and Privacy Policy

The rate at which the volume of the ice cube is changing when the sides are 2 mm each is ( -24 , \text{mm}^3/\text{sec} ).

By signing up, you agree to our Terms of Service and Privacy Policy

- The radius of a spherical balloon is increasing at a rate of 2 centimeters per minute. How fast is the volume changing when the radius is 14 centimeters?
- How do you minimize and maximize #f(x,y)=x+y# constrained to #0<x+3y<2#?
- What is the maximum volume of the box, given the parameters below?
- A market survey suggests that, on the average, one additional unit will remain vacant for each 3 dollar increase in rent. Similarly, one additional unit will be occupied for each 3 dollar decrease in rent. What rent should the manager charge to maximize?
- How do you find the point on the graph of #x^2−2x=15−y^4# has the largest y-coordinate?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7