The ratio of the length to the breadth to the height of a box is 5 : 3 : 4. If the length is 12 cm longer than the breadth, find its volume.Volume: ____ cm³.

Step 1: Understand the problem

The problem gives us the ratio of the length, breadth, and height of a box as 5:3:4. It also tells us that the length is 12 cm longer than the breadth. We are asked to find the volume of the box.

Step 2: Define the variables

Let's denote the common ratio as x. So, the length of the box is 5x, the breadth is 3x, and the height is 4x.

Step 3: Set up the equation

According to the problem, the length is 12 cm longer than the breadth. So, we can write the equation as:

5x = 3x + 12

Step 4: Solve the equation

Solving the equation for x gives:

5x - 3x = 12 2x = 12 x = 12 / 2 x = 6

Step 5: Find the dimensions of the box

Now that we know x, we can find the length, breadth, and height of the box:

Length = 5x = 56 = 30 cm Breadth = 3x = 36 = 18 cm Height = 4x = 4*6 = 24 cm

Step 6: Find the volume of the box

The volume of a box is given by the formula:

Volume = Length * Breadth * Height

So, the volume of the box is:

Volume = 30 cm * 18 cm * 24 cm = 12960 cm³.