Question

A box has a width of 10 cm and a length of 17 cm. The volume of the box is decreasing at a rate of 527 cubic cm per minute, with the width and length being held constant. What is the rate of change, in cm per minute, of the height when the height is 6 cm

Answer 1

Answer:

$-3.1$ cm per minute.

Step-by-step explanation:

We have been given that a box has a width of 10 cm and a length of 17 cm. The volume of the box is decreasing at a rate of 527 cubic cm per minute, with the width and length being held constant.

We know that volume of a cuboid is length times width times height.

$V=lwh$

Upon substituting our given width and length, we will get:

$V=17\cdot 10\cdot h$

$V=170\cdot h$

Now, we will find derivative of volume with respect to time as:

$\frac{dV}{dt}=170\cdot \frac{dh}{dt}$

Since the volume of the box is decreasing at a rate of 527 cubic cm per minute, so we will substitute $\frac{dV}{dt}=-527$  as:

$-527=170\cdot \frac{dh}{dt}$

$\frac{-527}{170}=\frac{170\cdot \frac{dh}{dt}}{170}$

$\frac{dh}{dt}=-3.1$

Therefore, the rate of change in height is $-3.1$ cm per minute.