Two prisms are similar with a scale factor of 1:4. Find the volume of the smaller prism given that the volume of the larger is 2400ft3.

600 ft³

Step-by-step explanation:

Given the scale factor 1:4, we know that the smaller prism will be 4 times smaller than the larger prism.

We can calculate the volume of the smaller prism by dividing 2,400 by 4.

2,400/4 = 600

37.5

Step-by-step explanation:

We are asked to find the volume of the smaller prism, and we know that the larger prism has a volume of 2400 cubic feet. We also know that the scale factor of the two prisms is 1:4. You may be tempted to set 1/4 equal to x/2400, but that is not what you should do. Remember that the volume ratio is , if the similarity ratio is a/b. Now, with this in mind, we know that the cube root of 2400 is 13.388659. Now, we can set 1/4 equal to x/13.388659. Solve for x by cross multiplying. 13.388659=4x. Divide both sides by 4. x=3.34716475. Then, we need to find the volume of the smaller prism, so we find the third power of x, or 3.34716475, which is approximately 37.5, which is your solution.