A rectangular prism has a volume of 250 cubic cm.What would the volume be if one dimension stayed the same, a second dimension was three times as long, and the third was twice as long?
450 cm3
To find the new volume of the rectangular prism, we need to consider how each dimension has changed.
Let's assume the dimensions of the original rectangular prism are length (l), width (w), and height (h).
Based on the given conditions, we know that:
- One dimension stays the same.
- A second dimension becomes three times as long.
- The third dimension becomes twice as long.
Given:
Original volume of rectangular prism = 250 cubic cm
We can express this information in mathematical form:
Original volume (V1) = l * w * h
New dimensions (l', w', h'):
l' = l (stays the same)
w' = 3w (second dimension becomes three times as long)
h' = 2h (third dimension becomes twice as long)
New volume (V2) = l' * w' * h'
Now, let's substitute the new dimensions into the formula for the new volume:
V2 = (l) * (3w) * (2h)
V2 = 6lwh
Since we have the original volume (V1 = 250 cm^3), we can set up an equation:
V2 = 6lwh = 250
Solving for V2:
6lwh = 250
V2 = 250 / (6lw)
Therefore, the volume of the new rectangular prism would be 250 / (6lw) cubic cm, where l is the unchanged dimension, w is the dimension that is three times as long, and h is the dimension that is twice as long.
lwh = 250
l(2w)(3h) = 6lwh = 6(250) = 1500