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1 year ago

The edges of a cube increase at a rate of 3 cm/s. How fast is the volume changing when the length of each edge is 40 cm?

Mathematics

1 answer:

OLga [1]1 year ago

7 0

Answer:

14400 cm³/s

Step-by-step explanation:

Find the rate of change of volume in terms of edge length, and evaluate the expression for the given conditions.

<h3>Rate of change of volume</h3>

V = s³ . . . . volume in terms of edge length (s)

dV/dt = 3s²·ds/dt . . . . . . derivative of volume with respect to time

For the given values of s and ds/dt, this is ...

dV/dt = 3(40 cm)²(3 cm/s) = 14400 cm³/s

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