Question

All edges of a cube are expanding at a rate of 6 centimeters per second. (a) How fast is the volume changing when each edge is 5 centimeter(s)

Answer 1

(a).The volume of cube is changing at the rate
`450 cm^3/s`

Explanation:

Let x be the side of cube

`(dx)/(dt)=6 cm/s`

We have to find the rate at which volume of cube changing when edge is 5 cm.

We know that

Volume of cube, V=
`x^3`

Differentiate w.r.t t

`(dV)/(dt)=3x^2(dx)/(dt)`

Substitute the values

`(dV)/(dt)=3(5)^2* 6`

`(dV)/(dt)=450 cm^3/s`

Hence, the volume of cube is changing at the rate
`450 cm^3/s`