176k views
1 vote
Sodium Chlorate crystals grow into cube shapes by allowing a solution of water and chlorate to slowly evaporate.

Determine the instant rate of change of volume (in square millimeters) of the crystal when the measure of its sides are 13 millimeters.

1 Answer

1 vote

Answer:To determine the instant rate of change of volume of a sodium chlorate crystal when the measure of its sides is 13 millimeters, we need to find the derivative of the volume formula with respect to the side length.

Since the crystal is in the shape of a cube, the volume formula is given by V = s^3, where V represents the volume and s represents the side length.

To find the derivative of V with respect to s, we can use the power rule of differentiation, which states that the derivative of s^n is n*s^(n-1).

Applying the power rule, we differentiate V = s^3 as follows:

dV/ds = 3s^(3-1)

= 3s^2

Now, we can substitute the given side length of 13 millimeters into the derivative equation to find the instant rate of change of volume:

dV/ds = 3(13^2)

= 3(169)

= 507 square millimeters

Therefore, when the measure of the sides of the sodium chlorate crystal is 13 millimeters, the instant rate of change of its volume is 507 square millimeters.

Step-by-step explanation:

User Jasbner
by
8.6k points