Chapter 12.4, Problem 13PSB

Solution

To Calculate: The volume of the cube

The volume of the cube is $\frac{1000\sqrt{3}}{9}$ unit ${}^3$

Given information:

The face diagonal = $10$

Formula used:

Here, we are using the formula:

Volume of cube = $a^3$

(Where, “a” is side)

Calculation:

Here, face diagonal = $10$

We know that,

Face diagonal = $\sqrt{3}a$

(Where, “a” is side)

  $\sqrt{3}a=10$

  $a=\frac{10}{\sqrt{3}}$

So, volume of the cube = $a^3$

➜ ${\left(\frac{10}{\sqrt{3}}\right)}^3$

➜ $\frac{1000}{3\sqrt{3}}\times \frac{3\sqrt{3}}{3\sqrt{3}}$

➜ $\frac{3000\sqrt{3}}{9\times 3}$

➜ $\frac{1000\sqrt{3}}{9}$ unit ${}^3$

Conclusion: Hence, the volume of the cube is $\frac{1000\sqrt{3}}{9}$ unit ${}^3$