In a rectangular prism, the length and width are multiplied by 4. What is the relationship of the volume of the resulting rectangular prism compared to the original volume of the rectangular prism?
Is the new volume 8 times geater than original?
To determine the relationship between the new volume and the original volume of the rectangular prism, we need to understand how volume is calculated and how it changes when the dimensions of the prism are multiplied.
The volume of a rectangular prism is given by the formula:
Volume = Length x Width x Height
In this case, the length and width are both multiplied by 4. Let's assume that the height remains the same. So, the new volume, denoted as V', can be calculated as follows:
V' = (Length x 4) x (Width x 4) x Height
= Length x Width x Height x 4 x 4
= (Length x Width x Height) x (4 x 4)
= V x 16
Therefore, the new volume is equal to the original volume multiplied by 16, not 8. This means that the new volume is 16 times greater than the original volume, not 8 times.
recall that the volume of a rectangular prism is given by
V = L*W*H
where
L = lenght
W = width
H = height.
if 4 is multiplied to both length and width, the new volume, V', is
V' = (4L)*(4W)*(H)
V' = 16*(L*W*H) or
V' = 16*V
thus the new volume is 16 times greater.
hope this helps~ :)