Q. 59 Some crystals have rhombohedral ... [FREE SOLUTION]

Chapter 10: Q. 59 (page 825)

Some crystals have rhombohedral structures. A rhombohedron is a parallelepiped in which all of the edge lengths are equal and each of the six faces is a congruent rhombus. Find the volumes of the rhombohedral crystals described in Exercises 58 and 59.
Each side length is 2 cm, and the acute angles in each face measure $45^{o}$ . (See the hint in the previous exercise.)

Short Answer

Expert verified

The volumes of the rhombohedral crystals is $3.6$ cubic centimetre .

Step by step solution

Step 1. Given Information

Some crystals have rhombohedral structures. A rhombohedron is a parallelepiped in which all of the edge lengths are equal and each of the six faces is a congruent rhombus. We have to find the volumes of the rhombohedral crystals.
Each side length is 1 cm, and the acute angles in each face measure $45^{鈼�}$ .

Step 2. We have to find the volumes of the rhombohedral crystals.

$V = a^{3} (1 - \cos 胃) \sqrt{1 + 2 \cos 胃}$

From the question $a = 2 and 胃 = 45^{o}$

localid="1649867974388" $V = {(2)}^{3} (1 - \cos 45^{o}) \sqrt{1 + 2 \cos 45^{o}} V = 8 (1 - \frac{1}{\sqrt{2}}) \sqrt{1 + 2 脳 \frac{1}{\sqrt{2}}} V = 8 (1 - \frac{1}{1.41}) \sqrt{1 + \sqrt{2}} V = 8 (1 - 0.71) \sqrt{1 + 1.41} V = 8 脳 0.29 \sqrt{2.41} V = 8 脳 0.29 脳 1.55 V = 3.596 V = 3.6$

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Short Answer

Step by step solution

Step 1. Given Information

Step 2. We have to find the volumes of the rhombohedral crystals.

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