Question

A solid metallic cube having a total surface area of 24 m² is uniformly heated. If its temperature is increased by 10°C, calculate the increase in the volume of the cube.

(Given: α = 5.0 × 10^-4°C^-1)

Options

•  2.4 × 10⁶Cm³

•  1.2 × 10⁵Cm³

•  6.0 × 10⁴Cm³

• 4.8 × 10⁵Cm³

Answer 1

1.2 × 10⁵Cm³

Explanation:

We have ΔV = V₀ λΔT

ΔV = a³.(3α)ΔT

Now, 6a² = 24 [∵ Total surface area of cube = 6a²]

⇒ a² = 4

⇒ a = 2

So, ΔV = 2³ (3 × 5 × 10^-4) × 10 

= 1200 × 10^-4m³ 

= 1200 × 10²cm³ 

= 1.2 × 10⁵cm³