the linear expansivity of the material of a cube is 12×10*-6 k-1, if the length of each side of the cube is 5cm, find the volume of one face of the cube and the volume of the cube when it's temperature is raised by 20k?
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answer : area of one face of the cube is 25.012 cm² and volume of the cube is 125.09 cm³ when its temperature is raised by 20K
given, coefficient of linear expansion,α = 12 × 10^-6/K
length of each side of the cube , a = 5cm
temperature change , ∆T = 20K
area of one face of the cube, A = a²
= a²(1 + 2α∆T) [ for temperature change ∆T]
= (5cm)²[1 + 2 × 12 × 10^-6 × 20]
= 25cm²[1 + 480 × 10^-6 ]
= 25 × 1.00048
= 25.012 cm²
volume of the cube , V = a³
= a³(1 + 3α∆T) [ for temperature change ]
= (5cm)³ [1 + 3 × 12 × 10^-6 × 20 ]
= 125 cm³ [1 + 720 × 10^-6 ]
= 125 cm³ × 1.00072
= 125 × 1.00072 cm³
= 125.09 cm³
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