if the volume of a rectangular prism is 420 cubic units what is its vilume if one dimension is halved a second dimension is reduced to one third its original length and a third dimension remains unchanged?
How would I do this?
original:
length --- x
width ---- y
height ---z
xyz = 420
new prism
length --- x/2
width ---- y/3
height --- z
(x/2)(y/3)z =
= xyz/6
= 420/6
= 70 units3
notice it wouldn't matter which dimensions are halved and cut into thirds, I could have used other combinations. The final result is that it would be 1/6 of the original
Well, let's solve this riddle, shall we? If the original volume of the rectangular prism is 420 cubic units, and we're playing around with the dimensions, the first thing we need to know is that volume is all about multiplication. So, let's call the original dimensions length (L), width (W), and height (H).
Now, if we halve one dimension, it means we divide it by 2. If we reduce another dimension to one-third its original length, it means we multiply it by 1/3. And if one dimension remains unchanged, well, it stays the same.
So, let's calculate the new volume, shall we? V2 = (L/2) * (W * 1/3) * H. But let's not forget that the original volume was 420 cubic units, so we can set up an equation:
420 = (L/2) * (W * 1/3) * H
Now, you'll need to work your mathematical magic and solve for V2. I wouldn't want to steal all the fun from you, my friend. Remember, math can be entertaining if you approach it with humor! Good luck!
To solve this problem, you can use the formula for the volume of a rectangular prism, which is given by:
Volume = Length × Width × Height.
Let's assume the original dimensions of the rectangular prism are Length (L), Width (W), and Height (H).
According to the given conditions:
- If one dimension is halved, let's say the Length:
New Length = L/2
- If a second dimension is reduced to one third its original length, let's say the Width:
New Width = W/3
- The third dimension remains unchanged, so the Height stays the same.
Now, we can calculate the new volume using the formula:
New Volume = (New Length) × (New Width) × (Height).
Substituting the given values in terms of the original dimensions, we obtain:
New Volume = (L/2) × (W/3) × (H)
Therefore, the final step is to substitute the given value of the original volume into the equation and solve for the new volume.
New Volume = (L/2) × (W/3) × (H) = 420 cubic units.
Please provide the values of the original dimensions (Length, Width, and Height) to calculate the new volume.
To find the new volume of the prism given the changes in dimensions, you need to follow these steps:
1. Identify the original dimensions of the prism, let's call them length (L), width (W), and height (H).
2. Use the formula for the volume of a rectangular prism: Volume = L × W × H.
3. Calculate the original volume by substituting the values into the formula.
4. To obtain the new dimensions, follow the given changes:
a. Halve one dimension: Divide the value of that dimension by 2.
b. Reduce another dimension to one third its original length: Multiply the value of that dimension by 1/3.
c. Keep the third dimension unchanged.
5. Substitute the new values into the formula for volume to find the new volume.
Let's apply these steps to the given problem:
1. Let L, W, and H represent the original length, width, and height of the prism, respectively.
2. The original volume formula is: Volume = L × W × H.
3. Given the volume of the prism is 420 cubic units, we have:
420 = L × W × H
4. Applying the changes:
a. Halving one dimension: Let's say we halve the length, so the new length is L/2.
b. Reducing another dimension to one third its original length: Let's say we reduce the width, so the new width is W × (1/3).
c. Keeping the third dimension unchanged, the height remains as H.
5. Substituting the new values into the formula for volume:
New Volume = (L/2) × (W × (1/3)) × H
Remember, the values of L, W, and H were not given, so we can only express the new volume in terms of the original dimensions and the given changes.