Question

The volume of a cuve is increasing at a constant ratec.Prove that the surface increasee vvaries inversly as the lenght of the edge

Answer 1

Answer:

Explanation:

2 Answers

Richa Ghosh

Richa Ghosh, BTech Technology, Netaji Subhash Engineering College (2018)

Answered Mar 20, 2017

From First Energy Theorem,

dQ= dU+pdv

Tds= dU+pdv

For v=c,

Tds= dU

Tds= Cvdt

T

Again, dh= T ds -v dp

Cp dT = T dS - vdp

For p=c

Cp dT = Tds

dT/dS = T/

As  

(dT/dS ; v=c ) > (dT/dS ; p=c)

Answer 2

Answer:

Explanation:

Step 1

Let the surface area of the cube be

S=6x2

and the volume of the cube be

v=x3

where x is the edge of the cube

v=x3

differentiating w.r.t x we get,

dvdt=3x2dxdt

But it is given that dvdt=k ( constant)

∴k=3x2dxdt⇒dxdt=k3x2

s=6x2

differentiating w.r.t x we get,

dsdt=12x.dxdt

Now substituting for dxdt we get,

dsdt=k3x2×12x

=4kx

⇒dsdtα1x