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)

विकल्प

•  2.4 × 10⁶ cm³

•  1.2 × 10⁵ cm³

•  6.0 × 10⁴ cm³

• 4.8 × 10⁵ cm³

Answer 1

1.2 × 10⁵ cm³

Explanation:

Given: α = 5.0 × 10⁻⁴°C⁻¹

ΔT = 10

Total surface area of the cube = 24 m²

⇒ 6a² = 24

⇒ a² = `24/6`

⇒ a² = 4    ...[Taking square root on both sides]

⇒ a = 2 m

Initial volume (V) = a³

= 2³

= 8 m

Volume expansion (ΔV) = 3αVΔT

= 3 × (5 × 10⁻⁴) × 8 × 10

= 0.12 m³

= 0.12 × 10⁶ cm³

= 1.2 × 10⁵ cm³