To find the rate of change in the volume of a cube with respect to its side, we can use the derivative. The volume (V) of a cube is given by the formula:
V = side^3
Now, let's find the derivative of the volume with respect to the side (s):
dV/ds = 3 * side^2
Given that the side (s) is 3 meters:
dV/ds = 3 * (3)^2
dV/ds = 3 * 9
dV/ds = 27 cubic meters per meter
So, the rate of change in volume of the cube with respect to its side when the side is 3 meters is 27 cubic meters per meter.
Answers & Comments
Answer:
To find the rate of change in the volume of a cube with respect to its side, we can use the derivative. The volume (V) of a cube is given by the formula:
V = side^3
Now, let's find the derivative of the volume with respect to the side (s):
dV/ds = 3 * side^2
Given that the side (s) is 3 meters:
dV/ds = 3 * (3)^2
dV/ds = 3 * 9
dV/ds = 27 cubic meters per meter
So, the rate of change in volume of the cube with respect to its side when the side is 3 meters is 27 cubic meters per meter.
Explanation:
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