Final answer:
The volume of the cube at 20°C is 125.5 cm³. Option a is correct.
Step-by-step explanation:
To find the volume of the cube at 20°C, we need to consider the expansion of the metal due to temperature increase.
The linear expansivity of the metal is given as 4.0*10^-5/K, which means that for every 1°C increase in temperature, the length of the metal will increase by 4.0*10^-5 times its original length.
Given that the length of a side of the cube at 20°C is 5.0 cm, we can calculate the increase in length due to a temperature increase of 20°C as follows:
Increase in length = (linear expansivity) * (original length) * (temperature increase)
Increase in length = (4.0*10^-5/K) * (5.0 cm) * (20°C)
Increase in length = 0.00004 * 5.0 * 20 cm
Increase in length = 0.004 cm
Since the cube has equal sides, the increase in length applies to all sides. Therefore, the new length of each side at 20°C would be:
New length = (original length) + (increase in length)
New length = 5.0 cm + 0.004 cm
New length = 5.004 cm
Now, we can calculate the volume of the cube at 20°C:
Volume = (side length)^3
Volume = (5.004 cm)^3
Volume = 125.5 cm³
Therefore, the volume of the cube at 20°C is 125.5 cm³.
So, the correct answer is option a) 125.5 cm³.