 |
| ||
| |||
|
| Math Central | Quandaries & Queries |
|
Question from Emily, a student: a cube of ice (i.e.) each side is of the same length) is melting at a rate such that the length of each side is decreasing at a rate of 5cm per hour. how fast is the volume of the cube decreasing (in cubic cm per hour) at the instant the length of each side is 25cm? |
Hi Emily,
Suppose that $t$ is time measured in hours. The side length is a function of time so I am going to write the side length as $s(t)$ cm. The side length is decreasing at the rate of 5 cm per hour so $s'(t) = -5$ cm per hour.
The volume of the cube is given by $V(t) = s(t)^3$ cubic centimeters. Differentiate this expression implicitly with respect to $t$ and then solve for $V'(t)$ when $s(t) = 25$ cm.
Penny
| ||
| ||
| ||
 |
 |
|
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.