Two boxes are similar. The larger box has a volume that is 64 times the volume of the smaller box. What is the ratio of the larger box's height to the smaller box's height? write the fraction as a decimal
What is the cube root of 64?
You won't need decimals. It is an integer.
The ratio of corresponding linear dimensions of similarly shaped volumes is the cube root of the volume ratio.
To find the ratio of the larger box's height to the smaller box's height, we can set up an equation using the given information.
Let's assume the height of the smaller box is "h". Then, the volume of the smaller box would be h^3.
According to the given information, the larger box has a volume that is 64 times the volume of the smaller box. So, the volume of the larger box would be (h^3) * 64.
Now, we know that the volume of a box is determined by multiplying the length, width, and height. Since the two boxes are similar, their lengths and widths are proportional. However, we are only concerned with the ratio of the heights.
Therefore, we can equate the volumes of the two boxes and solve for the ratio of their heights:
(h^3) * 64 = h^3
Divide both sides of the equation by h^3:
64 = 1
This equation implies that 64 = 1, which is not true. Therefore, this scenario is not possible.
As a result, there is no ratio of heights, and we cannot express it as a decimal fraction.