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?

Options

A. `900 cm^(3)//s`
B. `920 cm^(3)//s`
C. `850 cm^(3)//s`
D. `950 cm^(3)//s`

Answer

A

Explanation

Let side of cube be x then `(dx)/(dt)=3 cm//s`
`:' V=x^(3) :. (dV)/(dt)=3x^(2) (dx)/(dt)=3xx10^(2)xx3=900 cm^(3)//s`