Question

Find the volume of a cube whose one of the diagonal is 2.5m

Answer 1

The volume of the cube is$\frac{15.625}{3\sqrt{3}} m^{3}$.

Step-by-step explanation:

Given,

Diagonal of a cube = 2.5 m

To find,  the volume of a cube = ?

Let side of cube = a

We know that,

Diagonal of a cube = $\sqrt{3} a$

⇒$\sqrt{3} a=2.5$

∴ a = $\dfrac{2.5}{\sqrt{3}}$ m

The volume of a cube = $a^{3}$

=$(\dfrac{2.5}{\sqrt{3}})^{3}$ $m^{3}$

= $\frac{15.625}{3\sqrt{3}} m^{3}$

$= \frac{15.625}{3\sqrt{3}} m^{3}$

Hence, the volume of the cube is$\frac{15.625}{3\sqrt{3}} m^{3}$.

Answer 2

Dear,

● Answer -

Volume of cube = 3.007 m³

● Explanation -

All diagonals of cube are equal.

Length of diagonal is related to side of cube as -

d = √3 a

2.5 = √3 a

a = 2.5/√3

Volume of the cube is calculated as -

V = a³

V = (2.5/√3)³

V = 15.625/3√3

V = 3.007 m³

Hence, volume of the cube is 3.007 m³.

Hope this helps you...