Chapter 12: Q38. (page 480)

A diagonal of a cube joins two vertices not in the same face. If the diagonals are $4 \sqrt{3}$ cm long, what is the volume?

Short Answer

Expert verified

The volume is $\frac{8 \sqrt{3}}{9} {cm}^{3}$ when the diagonals are $4 \sqrt{3} cm$ .

Step by step solution

Step 1. Given information.

A diagonal of a cube joins two vertices not in the same face and the diagonals are $4 \sqrt{3} cm$ long.

Step 2. Write the concept.

Since a diagonal of a cube joins two vertices not in the same face.

Then, the factor can be found as:

$\begin{matrix} k = \frac{4 \sqrt{3}}{2} \\ = 2 \sqrt{3} cm \end{matrix}$

Step 3. Determine the volume.

Now, the ratio of the larger cube and smaller cube is cube of k factor,

$\begin{matrix} \frac{v_{l}}{v_{s}} = k^{3} \\ \frac{{(4 \sqrt{3})}^{2}}{v_{s}} = {(2 \sqrt{3})}^{3} [simplify] \\ \frac{64}{v_{s}} = 24 \sqrt{3} [multiply] \end{matrix}$

Simplify the last expression,

$\begin{matrix} v_{s} = \frac{64}{24 \sqrt{3}} [crossmultiplication] \\ = \frac{8 \sqrt{3}}{9} [simplify] \end{matrix}$

Thus, the volume is $\frac{8 \sqrt{3}}{9} {cm}^{3}$ when the diagonals are $4 \sqrt{3} cm$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

A diagonal of a cube joins two vertices not in the same face. If the diagonals are $4 \sqrt{3}$ cm long, what is the volume?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Determine the volume.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Statistics

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

A diagonal of a cube joins two vertices not in the same face. If the diagonals are43cm long, what is the volume?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Determine the volume.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Statistics

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

A diagonal of a cube joins two vertices not in the same face. If the diagonals are $4 \sqrt{3}$ cm long, what is the volume?