A box of height 8cm has a volume of 320cm cube.What is the volume of a similar box of height 6cm
320*6=1920
1920/8=240cm^3
The volume of 2 similar objects is proportional to the cube of its linear sides
320/x = 8^3/6^3
512x = 69120
x = 69120/512 = 135
or
the side ratio is 6/8 = 3/4
old volume = 8(l)(w) = 320
lw = 40
new volume = 6(3l/4)(3w/4) = 54/16 lw
= (54/16)(40)
= 135
Thanks
To determine the volume of a similar box of height 6cm, we first need to understand the relationship between the volume and the height of the boxes.
The volume of a box is calculated by multiplying its length, width, and height. In this case, you have the volume (320 cm³) and the height (8 cm) of one box.
Since the boxes are similar, the ratio of their heights will be the same as the ratio of their volumes. This means that if the height of one box is altered by a certain factor, the volume will change by the same factor.
To find the volume of the second box with a height of 6cm, we need to find the ratio between the two heights and use it to scale the volume.
Ratio of heights: 8 cm ÷ 6 cm = 4/3
Since the height ratio is 4/3, the volume ratio will also be 4/3. So, to find the volume of the second box, we multiply the volume of the first box (320 cm³) by the volume ratio (4/3).
Volume of second box = 320 cm³ × 4/3
= (320 × 4) / 3
= 1280 / 3
≈ 426.67 cm³ (rounded to 2 decimal places)
Therefore, the volume of a similar box with a height of 6cm is approximately 426.67 cm³.
Well, to find the volume of the similar box of height 6cm, we can use some proportional reasoning. If the original box has a height of 8cm and a volume of 320cm cube, we can set up the following ratio:
Volume of original box / Height of original box = Volume of similar box / Height of similar box
Simplifying the ratio, we get:
320cm cube / 8cm = x / 6cm
Now, let's do some math magic:
320cm cube / 8cm = 40cm cube
So, the volume of the similar box of height 6cm would be 40cm cube.
Just remember, all boxes may not be the same, but they're always ready to think inside the box!