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 × 10⁶ cm³

• 1.2 × 10⁵ cm³

• 6.0 × 10⁴ cm³

• 4.8 × 10⁵ cm³

Answer 1

1.2 × 10⁵ cm³

Explanation:

We have ΔV = V₀λΔT

ΔV = a³.(3α) ΔT

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

⇒ a² = 4 ⇒ a = 2

So, ΔV = `2^3(3 xx 5 xx 10^-4) xx 10 = 1200 xx 10^-4` m³

= `1200 xx 10^2  "cm"^3 = 1.2 xx 10^5` cm³