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## Homework Statement

Dear All,

I am having problems understanding how to deal with related rates. The problem is the following:

A solid 400gm metal cube of size length 10cm expands uniformly when heated. If the length of its side expand at 0.5cm(hr), find the rate at which, after 5 hours, its volume will increase.

## Homework Equations

## The Attempt at a Solution

What I need to know is how the Volume will increase after five hours. Hence:

[tex]\frac{dV}{dt}[/tex]

As

[tex]V=S^3[/tex]

(V = Volume, S = Side, T = Time)

Then

[tex]\frac{dV}{dt} = 3L^2\frac{dS}{dt}[/tex]

Which is equal to

[tex]3L^2*0.5[/tex]

As to find the length of the sides:

[tex]f(S) = 10+0.5(T)[/tex]

Where T is time in hours. However, by substituting values I don't obtain the correct answer. Any help? :(