Question

The edges of a cube increase at a rate of 2 cm divided by s. How fast is the volume changing when the length of each edge is 40 ​cm? Write an equation relating the volume of a​ cube, V, and an edge of the​ cube, a. nothing Differentiate both sides of the equation with respect to t. StartFraction dV Over dt EndFraction equals(nothing )StartFraction da Over dt EndFraction ​(Type an expression using a as the​ variable.) The rate of change of the volume is nothing cm cubed divided by sec. ​(Simplify your​ answer.)

Answer 1

Explanation:

Let the edge of the cube be a .

Given

`(da)/(dt) = 2 cm/s`

Volume V = a³

`(dV)/(dt) = 3a^ 2(da)/(dt)`

= 3a² x 2

= 6a²

If a = 40 cm

`(dV)/(dt) = 6 * 40*40`

= 9600 cm³/s .