the volume of a rectangular prism is 256 cubic centimeters. What is the volume of a similar rectangular prism that has edge lengths one fourth as long as the edge lengths of the original prism?

dimensions were a,b,c, volume was v = a*b*c

new volume is (a/4)(b/4)(c/4) = abc/64 = v/64

if edges are scaled by f,
area is scaled by f^2
volume is scaled by f^3

To find the volume of the similar rectangular prism, we need to apply the principle of similarity. The volume of a rectangular prism is given by the formula:

Volume = length × width × height

Let's assume the edge lengths of the original prism are represented by:
length = L
width = W
height = H

Given that the volume of the original prism is 256 cubic centimeters, we have the equation:

256 = L × W × H Eq. (1)

Now, we are given that the edge lengths of the new prism are one fourth as long as the original prism. Therefore, the new dimensions can be represented as:

length of new prism = L/4
width of new prism = W/4
height of new prism = H/4

To find the volume of the new prism, let's substitute these values into the volume formula:

Volume of new prism = (L/4) × (W/4) × (H/4)

Simplifying this expression, we can rewrite it as:

Volume of new prism = (L × W × H) / (4 × 4 × 4)

Using Eq. (1), we can substitute the value of the volume of the original prism:

Volume of new prism = 256 / (4 × 4 × 4)

Calculating further:

Volume of new prism = 256 / 64

Volume of new prism = 4 cubic centimeters

Therefore, the volume of the similar rectangular prism with edge lengths one fourth as long as the edge lengths of the original prism is 4 cubic centimeters.

To find the volume of the similar rectangular prism, we need to know the edge length of the original prism.

Let's assume that the edge lengths of the original prism are given by the variables "length," "width," and "height." Therefore, the volume of the original rectangular prism can be calculated as V = length * width * height.

Given that the volume of the original rectangular prism is 256 cubic centimeters, we have V = 256.

To find the volume of the similar prism, we know that the edge lengths of the new prism are one fourth as long as the edge lengths of the original prism.

This means the edge length of the similar prism is length/4, width/4, and height/4.

Therefore, the volume of the similar rectangular prism can be calculated as V_similar = (length/4) * (width/4) * (height/4).

Let's substitute V = 256 into the equation:

V_similar = (length/4) * (width/4) * (height/4) = 256

By simplifying the equation, we can solve for V_similar:

(length * width * height) / (4 * 4 * 4) = 256

(length * width * height) / 64 = 256

(length * width * height) = 256 * 64

(length * width * height) = 16384

Therefore, the volume of the similar rectangular prism is 16384 cubic centimeters.