Chapter 12: Q35. (page 480)

A right prism has height x and bases that are equilateral triangles with sides x. Show that the volume is $\frac{1}{4} x^{3} \sqrt{3}$ .

Short Answer

Expert verified

The volume of the prism is $\frac{1}{4} x^{3} \sqrt{3}$ .

Step by step solution

Step 1. Given information.

Right prism height is x and base have equilateral triangles with side x.

Step 2. Write the concept.

Since base have equilateral triangles, then

$B = \frac{\sqrt{3}}{4} x^{2}$

Step 3. Determine the volume.

Now, the volume of the right prism is:

$\begin{matrix} v = B h \\ = \frac{\sqrt{3}}{4} x^{2} (x) [substitute] \\ = \frac{1}{4} x^{3} \sqrt{3} [multiply] \end{matrix}$

This is the required expression.

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 right prism has height x and bases that are equilateral triangles with sides x. Show that the volume is $\frac{1}{4} x^{3} \sqrt{3}$ .

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

Decision Maths

Calculus

Statistics

Geometry

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

A right prism has height x and bases that are equilateral triangles with sides x. Show that the volume is14x33.

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

Decision Maths

Calculus

Statistics

Geometry

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

A right prism has height x and bases that are equilateral triangles with sides x. Show that the volume is $\frac{1}{4} x^{3} \sqrt{3}$ .