Question

When a solid metallic sphere is heated the largest percentage increase occur in its?

Answer 1

Volume is the answer you are looking for.

When a solid metallic sphere is heated, it expands and hence its radius also increases.

We know that for a sphere,

Volume = $\frac{4}{3}$ $\pi$ $r^{3}$

and

Area = 4 $\pi r^{2}$

Thus, 
Volume $\alpha$ $r^{3}$
and
Area $\alpha$ $r^{2}$

Percentage change in volume:
ΔV/V = 3  Δr/r

Percentage change in Area:
ΔA/A = 2  Δr/r

Change in density:
Density decreases as on heating, the mass remains same but volume increases (Density = Mass/Volume)

Upon observation above, we see that Volume has the highest increase among all the physical quantities. Thus, Volume is the correct answer.

Answer 2

Answer Is : Volume

Explanation:

⇒When a solid metallic sphere is heated,  its diameter , surface area and volume will increases.

⇒As we know that density=mass/volume

⇒Here mass of the solid sphere remains unchanged . So its density decreases.

⇒Hence the  percentage increase in its volume is greater because Coefficient of Volume expansion is greater than coefficient of area expansion and Linear expansion.