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Calculus/related rates

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Expert: - 3/24/2009


Question
All edges of a cube are expanding at the rate of 3 cm per second. How fast is the surface area changing when each edge is 10 cm?

Answer
A cube has six faces.  

The lenth of each side is x.

The surface area of each face is x².

There are six faces on a cube.

The surface area of a cube S(x) is 6x².

The derivative of the equation for surface area is S'(x) = 12x.

The rate of change of area is the derivative of the area function.

When the side is 10cm, put 10cm in for x.
This would give us S'(x) = 12*10 = 120.  

Calculus

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