the linear expansively of the material of a cube is 12*10-6k. if the length of each side of the cube is 10cm,find the area of one face of the cube and the volume of the cube when its temperature is raised by 30k
No answer o
yes
To find the area of one face of the cube, we can simply square the length of one side of the cube. Given that the length of each side of the cube is 10 cm, the area of one face will be 10 cm multiplied by 10 cm, which is equal to 100 square cm.
To find the volume of the cube after the temperature is raised by 30K, we need to consider the linear expansivity of the material. The formula for linear expansion is given by:
ΔL = α * L * ΔT
where ΔL is the change in length, α is the linear expansivity coefficient, L is the original length, and ΔT is the change in temperature.
Given that the linear expansivity coefficient (α) is 12 * 10^-6 / K, the original length (L) is 10 cm, and the change in temperature (ΔT) is 30 K, we can calculate the change in length (ΔL) using the formula:
ΔL = (12 * 10^-6 / K) * (10 cm) * (30 K)
= 0.00012 cm/K * 10 cm * 30 K
= 0.036 cm
Now, the final length (L') of each side of the cube will be:
L' = L + ΔL
= 10 cm + 0.036 cm
= 10.036 cm
Therefore, the volume of the cube after the temperature is raised by 30K can be calculated by cubing the final length of each side:
Volume = (10.036 cm)^3
= 10.108 cm^3
So, the volume of the cube when its temperature is raised by 30K is approximately 10.108 cubic cm.
as with all geometric objects, the volume grows as the cube of the linear scale factor.
I assume your coefficient is 12*10^-6 cm/°K (can't quite tell from your notation). Anyway, if the linear size grows by 1.0002, then the area grows by 1.0002^2 and the volume grows by 1.0002^3, so multiply the base values by those scale factors.