The dimensions of a cuboid are in the ratio 6:3:2 . Its volume is 2.304 m*m*m. Find the dimensions and hence the total surface area of cuboid

Step 1: Understand the problem

The problem states that the dimensions of a cuboid are in the ratio 6:3:2 and its volume is 2.304 m^3. We are asked to find the dimensions and the total surface area of the cuboid.

Step 2: Find the dimensions

Let's denote the dimensions of the cuboid as 6x, 3x, and 2x. The volume of a cuboid is given by the product of its dimensions, so we have:

6x * 3x * 2x = 2.304

This simplifies to:

36x^3 = 2.304

Solving for x gives:

x^3 = 2.304 / 36 = 0.064

Taking the cube root of both sides gives:

x = cube root of 0.064 = 0.4

So, the dimensions of the cuboid are 6x = 2.4 m, 3x = 1.2 m, and 2x = 0.8 m.

Step 3: Find the total surface area

The total surface area of a cuboid is given by the formula:

2lw + 2lh + 2wh

Substituting the dimensions we found gives:

2(2.41.2) + 2(2.40.8) + 2(1.2*0.8) = 5.76 + 3.84 + 1.92 = 11.52 m^2

So, the total surface area of the cuboid is 11.52 m^2.