An edge of a variable cube is increasing at the rate of 10cm/sec. How fast the volume of the cube is increasing when the edge is 5cm long?

Options

A. 750`cm^(2)//s`
B. 75 `cm^(3)//s`
C. 300 `cm^(3)//s`
D. 150 `cm^(3)//s`

Answer

A

Explanation

let l be the length of an edge and V be the volume of cube at any time t.
`becauseV=l^(3)`
`therefore(dV)/(dt)=3l^(2)(dl)/(dt)`
`=3xx5^(2)xx10cm^(3)//s`
`=750cm^(3)//s`