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

Explanation

Let `x` be the length of a side and V be the volume of the cube.

Then, `V=x^{3}`
`
frac{d V}{d t}=3 x^{2} cdot frac{d x}{d t},`(By chain rule)

It is given that,


`frac{dx}{dt}=3 (cm) / s `
`
frac{dV}{dt}=3 x^{2}(3)=9 {x}^{2}`
`

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