It takes 154 cubes with side lengths of 1/2 inch to fill a rectangular prism. What is the volume of the rectangular prism? Show your work or justify your solution.

The volume of the rectangular prism is 19.25 inches³.

Step-by-step explanation:

Given:

It takes 154 cubes with side lengths of 1/2 inch to fill a rectangular prism.

Now, to find the rectangular prism's volume.

We first find the volume of a cube to fill in the rectangular prism.

The side length of the cube =

Now, to get the volume of cube we put formula:

Thus, the volume of a cube is  

Number of cubes = 154.

According to question, it takes 154 cubes to fill the rectangular prism.

So, to get the volume of prism we need to find the volume of 154 cubes.

Now, to get the volume of 154 such cubes we multiply the volume of a cube by number of cubes:

Therefore, the volume of the rectangular prism is 19.25 inches³.

it is true

step-by-step explanation:

all the combinations add up i used   calculator

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.