The width of the box in the form of a rectangular parallelepiped is 4 dm, which is 25%

The width of the box in the form of a rectangular parallelepiped is 4 dm, which is 25% of the height of the box, and the height, in turn, is 25% of the length. Calculate the volume of the box.

We need to find the volume. The volume is found by multiplying the length, width and height by each other. From all of the above, we need to find the length and height. Since there is a problem with percentages, it will be convenient to find the unknown using proportion.

First, let’s find the height of the box. We know the width is 4 cm and we know that it is 25% of the height. Let’s make a proportion.

4 dm – 25%.

x dm – 100%.

Let’s turn the proportion into an equation and solve it. To do this, we multiply the parts of the “cross – cross” proportion.

25x = 4 * 100.

25x = 400.

x = 400: 25.

x = 16 – dm box height.

Now let’s find the length in the same way. Let’s make a proportion and get the result.

16 dm – 25%.

x dm – 100%.

Now let’s also turn the proportion into an equation and solve it.

25x = 16 * 100.

25x = 1600.

x = 1600: 26.

x = 64 – dm box length.

Now that we know all the necessary terms, we find the volume.

4 * 16 * 64 = 4,906 (dm3).

Answer: 4 906 dm3 box volume.