If the edge of a cube increases at the rate of `60cm` per second, at what rate the volume in increasing when the edge is `90cm`

Options

A. `486000cm^(3)s^(-1)`
B. `1458000cm^(3)s^(-1)`
C. `43740000cm^(3)s^(-1)`
D. None of the above

Answer

B

Explanation

Given `(da)/(dt)=60cms^(-1)`, where a is edge and `t` is time.
Volume of cube `V=a^(3)`
`:.(dV)/(dt)=3a^(2)(da)/(dt)=3a^(2)xx60=180a^(2)`
`=180xx(90)^(2)=145800cm^(3)s^(-1)`