Question

The surface area of a cube increases at the rate of 12 cm²/sec. Find the rate at which its volume increases,when its edge has length 5 cm.

Answer 1

complete solution of the given question

Answer 2

Answer:

10 cm³/sec

Step-by-step explanation:

Let the side length, total cross-sectional area and the volume of the cube are given by a, A, V respectively.

Hence, A=6a² ....... (1)

and V= a³ ..........(2)

Now, differentiating equation (1) with respect to time(t), we get,

dA/dt=12a(da/dt) ....... (3)

Now, given that dA/dt=12 cm²/sec.

Hence, from equation (3), da/dt= 1/a.

Again, differentiating equation (2) with respect to time(t), we get,

dV/dt=3a² (da/dt) =3a²/a {Since da/dt=1/a}

⇒dV/dt= 3a.

Therefore, the rate of increase of volume (dV/dt) at a=5 cm, will be =2*5 =10 cm³/sec. (Answer)