The shortest edge of a rectangular prism is 3 inches, and its volume is 144 cubic inches. A similar rectangular prism has its shores edge equal to 4 inches. What is the approximate volume of the second prism?

The volume of similar 3-D solids is proportional to the cube of their corresponding sides, so

V/144 = 4^3/3^3
V = 144(64/27) = appr 341.33 in^3

or
original: 144 = 3lh
lh = 144/3

new: increased by a factor of 4/3
width = 4
length = (4/3)l
height = (4/3)h
new volume = 4(4/3l)(4/3h)
=(64/9)lh
= (64/9)(144/3) = 341.33

1.09375

To find the approximate volume of the second prism, we can use the concept of similarity in geometry. Similar shapes have proportional corresponding sides.

Let's denote the length of the shortest edge of the second prism as x inches.

Since the two rectangular prisms are similar, we can set up a proportion using the lengths of their corresponding sides:

3 / x = 144 / V,

where V is the volume of the second prism.

We can cross-multiply to solve for V:

3V = 144 * x,

V = (144 * x) / 3,

V = 48x.

Now, we can substitute the value of x with 4 inches, the length of the shortest edge of the second prism:

V ≈ 48 * 4,

V ≈ 192 cubic inches.

Therefore, the approximate volume of the second prism is approximately 192 cubic inches.

To find the approximate volume of the second prism, we can use a concept called similarity. Similar shapes have the same shape but possibly different sizes. In this case, we have two rectangular prisms that are similar.

Let's compare the ratio of the shortest edges of the two prisms. The first prism has a shortest edge of 3 inches, and the second prism has a shortest edge of 4 inches. The ratio is 3:4.

Since the prisms are similar, the ratio of their corresponding side lengths must be the same as the ratio of their shortest edges. This means that the ratio of the volumes of the two prisms is the cube of the ratio of their side lengths.

So, to find the volume of the second prism, we can set up the following equation:

(4/3)^3 = (Volume of the second prism)/(144 cubic inches)

Simplifying:

64/27 = (Volume of the second prism)/(144 cubic inches)

To find the volume of the second prism, we can cross-multiply and solve for it:

Volume of the second prism = (64/27) * 144 cubic inches

Now, we can calculate the approximate volume of the second prism:

Volume of the second prism ≈ 340.44 cubic inches