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

Explanation

`V=x^{3}`



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


It is given that,



`frac{d x}{d t}=3 {cm} / {s} `


`therefore frac{d V}{d t}=3 x^{2}(3)=9 x^{2}`



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