Question

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?

Answer 1

It is given that an edge of a variable cube is increasing at the rate of 3 cm/s.

Let the side of the cube be x cm. So, the volume of cube is V= x 3 .

Differentiate volume V with respect to the time t.

dV dt = d( x 3 ) dt =3 x 2 dx dt

It is given that dx dt =3. Therefore,

dV dt =3 x 2 ( 3 ) =9 x 2

Substitute x=10 cm in the above equation.

dV dt =9 ( 10 ) 2 =900

Thus, the volume of the cube is increasing at the rate of 900  cm 3 /s.