What is a general strategy to find dimensions for any rectangular box whose volume is doubled?
MY THOUGHTS IS 2L by 2w by 2h
Sounds good.
Yes sounds good
To find the dimensions of a rectangular box whose volume is doubled, you can follow these steps:
1. Start with the formula for the volume of a rectangular box: V = l × w × h, where l, w, and h represent the length, width, and height of the box.
2. Let's assume the initial dimensions are l1, w1, and h1, and the initial volume is V1.
3. According to the problem, we want to double the volume (V1) of the box. So, the new volume (V2) will be 2 times the initial volume: V2 = 2 × V1.
4. Substitute the formula for volume into the equation: V2 = 2 × l1 × w1 × h1.
5. Rearrange the equation to solve for the unknown dimensions: (l1 × w1 × h1) = (V2 / 2).
6. Take the cube root of both sides of the equation to isolate the variables: l1 × w1 × h1 = (V2 / 2)^(1/3).
7. Now, we have a relationship between the original dimensions and the new volume: l1 × w1 × h1 = (V2 / 2)^(1/3).
8. Calculate the cube root of (V2 / 2) to find the side length of each dimension: l1 = w1 = h1 = (V2 / 2)^(1/3).
Therefore, the general strategy to find the dimensions of a rectangular box whose volume is doubled is to calculate the cube root of half the new volume and assign this value to each dimension (length, width, and height).
To find the dimensions for a rectangular box whose volume is doubled, you can follow this general strategy:
1. Start with the initial dimensions of the rectangular box, typically denoted as length (L), width (w), and height (h).
2. Calculate the initial volume of the rectangular box using the formula: Volume = L * w * h.
3. Double the initial volume to find the desired new volume for the box.
4. Set up an equation using the new volume and the initial dimensions: (2 * Volume) = L * w * h.
5. Rearrange the equation to solve for one of the dimensions. You can choose any dimension to solve for.
6. Once you have the value for one dimension, you can choose another dimension to solve for. Keep in mind that multiplying the values of any two dimensions should equal the initial volume.
7. Repeat the process for the remaining dimensions.
For example, let's say the initial dimensions of the rectangular box are L = 10 units, w = 5 units, and h = 3 units. The initial volume is: Volume = 10 * 5 * 3 = 150 cubic units.
Let's say you want to double the volume to reach 300 cubic units:
(2 * Volume) = 300 cubic units.
Now you can rearrange the equation to solve for one dimension. Let's solve for the length (L):
2 * 150 = L * 5 * 3.
300 = 15L.
L = 20 units.
Now you have the value for one dimension, and you can choose another dimension to solve for. Let's solve for the width (w):
w = 300 / (20 * 3) = 5 units.
Finally, solve for the height (h) by dividing the initial volume by the new dimensions:
h = 300 / (20 * 5) = 3 units.
Therefore, the new dimensions for the doubled volume of the rectangular box are L = 20 units, w = 5 units, and h = 3 units.