StudyGPT Just Leveled Up – Say Hello to Knowee! 🚀
Knowee
Questions
Features
Study Tools

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

Question

🧐 Not the exact question you are looking for?Go ask a question

Solution

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.

This problem has been solved

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.