Question

An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the
volume of the cube increasing when the edge is 10 cm long?

Answer 1

@terenzreignz

Answer 2

okay... if we let x be the length of one edge of the cube, we get that the volume of the cube is equal to...
\[\huge V = x^3\]
Now... we're looking for
\[\huge \left.\frac{dV}{dt}\right.\]

Answer 3

Differentiating seems simplest...
\[\huge \frac{dV}{dt}=\frac{dV}{dx}\times \frac{dx}{dt}\]
And we do have a value for the dx/dt... it's just 3.

So once this is done, plug in x = 10, and you're all set.

Answer 4

Thankyou sir