the volume of a larger prism is 128 cubic cm. if the prisms are similar with linear ration of 4:3, what is the volume of the smaller prism?
We have a theorem that says
The volumes of similar objects are proportional to the cubes of their sides.
So let the volume of the smaller prism be V
then V/128 = 3^3 / 4^3
V/128 = 27/64
cross-multiply and solve
To find the volume of the smaller prism, we can set up a proportion using the theorem that states the volumes of similar objects are proportional to the cubes of their sides.
Let the volume of the smaller prism be V. We know that the linear ratio between the larger prism and the smaller prism is 4:3.
Therefore, the ratio of the volumes of the larger prism and the smaller prism is (4/3)^3.
We can set up the proportion:
V/128 = (4/3)^3/1
To solve for V, we can cross-multiply:
V = 128 * (4^3/3^3)
Simplifying the right side of the equation:
V = 128 * (64/27)
V = 128 * 2.37037...
V ≈ 303.7037...
Therefore, the volume of the smaller prism is approximately 303.7 cubic cm.