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all the edges of a cube are expanding at a rate of 4 in. per second. how fast is the volume changing when each edge is 10in. long?

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The rate at which the volume of the cube is changing is 1200 in³/seconds.

What is volume?

Volume is the space occupied by a solid object.

To calculate the rate at which the volume of the cube is changing, we use the formula below.

Formula:

  • dV/dt = (dL/dt)×(dV/dL)................ Equation 1

Where:

  • dV/dt = Rate at which the volume of the cube is changing
  • dL/dt = Rate at which the edge of the cube is expanding
  • dV/dL = Change in the volume of the cube with respect to the edge.

From the question,

Given:

  • dL/dt = 4 in. per seconds
  • L = 10 in

If, the volume of a cube is V = L³,

Then,

  • dV/dL = 3L²  = (3×10²) = 300 in²

Substitute these values into equation 1

  • dV/dt = 4×300
  • dV/dt = 1200 in³/seconds

Hence, the rate at which the volume is changing is 1200 in³/seconds.
Learn more about volume here: https://brainly.com/question/1972490

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