A rectangular solid has a volume of 40 cubic centimeters. If the dimensions are all reduced to 1/2 their original size, what will be the new volume of the rectangular solid?

1/2*1/2*1/2 = 1/8

To find the new volume of the rectangular solid after reducing the dimensions to 1/2 their original size, we need to understand the relationship between volume and dimensions.

The volume of a rectangular solid is calculated using the formula:

Volume = length * width * height

We are given that the original volume of the rectangular solid is 40 cubic centimeters. Let's assume the original dimensions are length (L), width (W), and height (H).

Therefore, the equation becomes:

40 = L * W * H

Now, we know that all dimensions are reduced by 1/2. So, the new dimensions will be:

new length (L') = L/2
new width (W') = W/2
new height (H') = H/2

To find the new volume (V') of the rectangular solid after reducing the dimensions, we substitute the new dimensions in the volume equation:

V' = (L/2) * (W/2) * (H/2)

To simplify the equation, we can rewrite it as:

V' = (L * W * H) / (2 * 2 * 2)

Since (2 * 2 * 2) equals 8, we can simplify further:

V' = (L * W * H) / 8

Given that the original volume is 40 cubic centimeters, we can substitute this value into the equation:

40 = (L * W * H) / 8

To find the value of the new volume (V'), we can solve this equation:

V' = 40 * 8

V' = 320 cubic centimeters

Therefore, the new volume of the rectangular solid, after reducing all dimensions to 1/2 their original size, is 320 cubic centimeters.