The length, breadth and height of a rectangular solid are in the ratio 5:4:2. If its total surface areais 1216 cm2, find the volume of the solid

Sure, let's solve this step by step.

Step 1: Understand the problem The problem gives us the ratio of the length, breadth, and height of a rectangular solid (also known as a rectangular prism or a cuboid). It also gives us the total surface area. We need to find the volume.

Step 2: Use the formulas The total surface area of a rectangular solid is given by the formula 2(lb + bh + hl), where l is the length, b is the breadth, and h is the height. The volume of a rectangular solid is given by the formula lbh.

Step 3: Set up the equations We know that l:b:h = 5:4:2, so we can say that l = 5x, b = 4x, and h = 2x for some value of x. We also know that the total surface area is 1216 cm^2. So we can set up the equation 2(5x4x + 4x2x + 5x*2x) = 1216.

Step 4: Solve for x Solving the equation gives us x = 8.

Step 5: Find the volume Now that we know x, we can find the volume by substituting l = 5x, b = 4x, and h = 2x into the volume formula. This gives us volume = 5x4x2x = 3200 cm^3.

So the volume of the solid is 3200 cm^3.