The volume of a rectangular solid is 250 cubic centimeters. If its length is tripled, its width is halved, and its height is quadrupled, what is the new volume, in cubic centimeters?
the old v is lwh
the new v is (3l)(w/2)(4h) = 6lwh
v = 6*250 = 1500
To find the new volume of the rectangular solid, we need to calculate the new dimensions of the solid after the given transformations and then use the formula for calculating the volume of a rectangular solid.
Let's start by determining the new dimensions:
1. Length: The original length of the solid is not given, so let's call it "L." According to the problem, the length is tripled, so the new length will be 3L.
2. Width: The original width of the solid is not given, so let's call it "W." According to the problem, the width is halved, so the new width will be W/2.
3. Height: The original height of the solid is not given, so let's call it "H." According to the problem, the height is quadrupled, so the new height will be 4H.
Now that we have the new dimensions, we can calculate the new volume using the formula:
Volume = Length × Width × Height
Substituting the new dimensions, we get:
New Volume = (3L) × (W/2) × (4H)
Simplifying the equation:
New Volume = 3 × 4 × (L × W × H) / 2
The original volume of the rectangular solid is 250 cubic centimeters, so we have:
250 = 3 × 4 × (L × W × H) / 2
Now, solve for (L × W × H):
250 = 12 × (L × W × H) / 2
To eliminate the division by 2, multiply both sides of the equation by 2:
500 = 12 × (L × W × H)
Finally, divide both sides by 12 to solve for (L × W × H):
(L × W × H) = 500 / 12
(L × W × H) = 41.67 cubic centimeters
Therefore, the new volume of the rectangular solid, after the given transformations, is approximately 41.67 cubic centimeters.