Chapter 12: Q39. (page 480)

All nine edges of right triangular prism are congruent. Find the length of these edges if the volume is $54 \sqrt{3} {cm}^{3}$ .

Short Answer

Expert verified

The length of the edges is6 cm.

Step by step solution

Step 1. Given information.

All nine edges of a right triangular prism are congruent.

Step 2. Write the concept.

Since nine edges of a right triangular prism are congruent.

To find the edges length, let edges length isx,

So, the base area is:

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

Step 3. Determine the volume.

Now, the volume is:

$\begin{matrix} v = b h \\ 54 \sqrt{3} = \frac{\sqrt{3}}{4} x^{2} (x) [substitute] \\ 54 \sqrt{3} = \frac{\sqrt{3}}{4} x^{3} [mutliply] \end{matrix}$

So,

$\begin{matrix} x^{3} = 216 [simplify] \\ x = 6 [cuberoot] \end{matrix}$

Then, the length of the edges is 6 cm when the volume is $54 \sqrt{3} {cm}^{3}$ .

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All nine edges of right triangular prism are congruent. Find the length of these edges if the volume is $54 \sqrt{3} {cm}^{3}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Determine the volume.

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All nine edges of right triangular prism are congruent. Find the length of these edges if the volume is543 cm3.

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

Discrete Mathematics

Probability and Statistics

Pure Maths

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

All nine edges of right triangular prism are congruent. Find the length of these edges if the volume is $54 \sqrt{3} {cm}^{3}$ .