Question

A solid sphere is uniformly heated then it's volume increases by ∆V and surface area by ∆A it's radius is

Answer 1

Answer:

Radius of the sphere is given as

$R = \frac{2\Delta V}{\Delta A}$

Explanation:

As we know that the volume of sphere is given as

$V = \frac{4}{3}\pi R^3$

so change in volume is given as

$\Delta V = 4\pi R^2\Delta R$

now similarly the area is given as

$A = 4\pi R^2$

so change in area is given as

$\Delta A = 8\pi R\Delta R$

now divide above two equations

$\frac{\Delta V}{\Delta A} = \frac{R}{2}$

so we have

$R = \frac{2\Delta V}{\Delta A}$

#Learn

Topic : Volume expansion

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