Question

The sides of a certain closed cube are increasing at a constant rate uniformly such that at the instant when the side-length is 25 cm, the rate of change for the volume enclosed within the cube is exactly equal to 3 cm/sec. The rate of change of the total surface area of the cube at that instant is


pls solve fast​

Answer 1

Given :  The sides of a certain closed cube are increasing at a constant rate uniformly such that at the instant when the side-length is 25 cm, the rate of change for the volume enclosed within the cube is exactly equal to 3 cm³/sec.

To find : The rate of change of the total surface  of the cube at that instant

Explanation:

Let say Side of cube  = a  

rate of increasing side =  da/dt   cm/s

Volume = Side³

=> V = a³

=> dV/dt  = 3a²(da/dt)

dV/dt  = 3 cm³/sec    a = 25 sec

=> 3  = 3(25)² (da/dt )

=>da/dt  = 1/25²

Surface area  = 6 (side)²

=> S = 6a²

=> dS/dt = 12a (da/dt)

dS/dt  at a = 25 cm

=> dS/dt  = 12 ( 25) / 25²

=> dS/dt = 12/25  cm/s

The rate of change of the total surface area of the cube at that instant is 12/25 cm/sec  =  0.48 cm/s

Learn more:

The ratio of linear to volume expansion of a cube is 1:12. Find side ...

https://brainly.in/question/19162448

हवा के बुलबुले की त्रिज्या,1/2 cm/sec की दर से बढ़ रही ...

https://brainly.in/question/16307270