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**Explain why the thermal expansion of a spherical shell made of a homogeneous solid is equivalent to that of solid sphere of the same material.**

I guess these equations would be of some help.

(ΔA)=A*2α*(ΔT)

α→ Coefficient of linear expansion.

A→ Area

T→ Temperature

(ΔV)=V*3α*(ΔT)

α→ Coefficient of linear expansion.

V→ Volume

T→ Temperature

I'm not sure if i understood the question right.

By "equivalent thermal expansion" i guess they mean to say the radius increases by same amount during the expansion.

So i set out relating the two radii.

Took two spheres, one hollow, the other solid, of same dimensions, i.e., same radii.

For the Shell,

(ΔA)=A*2α*(ΔT)

R

R

For the solid sphere, similarly, relating the volume,

R

I'm not sure if i understood the question right.

By "equivalent thermal expansion" i guess they mean to say the radius increases by same amount during the expansion.

So i set out relating the two radii.

Took two spheres, one hollow, the other solid, of same dimensions, i.e., same radii.

For the Shell,

(ΔA)=A*2α*(ΔT)

R

_{f}^{2}-R_{i}^{2}=R_{i}^{2}*2α*ΔTR

_{f}=R_{i}√(2α*ΔT+1)For the solid sphere, similarly, relating the volume,

R

_{f}=R_{i}∛(3α*ΔT+1)But, failed to prove them to be the same.

So what exactly do they intend to ask? And how do i hit it?...