Question

length of diagonal of a cube is 3√3 cm then its volume is

Answer 1

Given :-

The diagonal of cube = 3√3 cm

To be found :-

The volume of the cube

The formula for finding diagonal of cube

= √3a    [ ∴ In which a is the side of the cube ]

So,

⇒ √3a = 3√3

⇒ a = $\frac{3\sqrt{3}}{\sqrt{3}}$

⇒ a = 3

Therefore,

Side of the cube = a = 3 cm

Now,

Volume of the cube = a³  unit cube.

[ ∴ In which a is the side of the cube ]

= (3)³ = 3 × 3 × 3

=  27 cm cube.

Hence,

The volume of the cube is 27 cm cube.

Answer 2

Given,

length of diagonal of square =

=$3 \sqrt{3}$

Refer to the attachment for diagram

Now,

Let the sides of square be x cm.

Since we know that the sides of square are perpendicular to each other, hence by using Pythagoras theorem in triangle ABC where Angle B=90°,we get =>

(AB)^2 + (BC)^2 = (AC)^2

=>x^2 + x^2 =
$( 3 \sqrt{3} ) {2}$

=>2x^2 = 9 ×2

=> x^2 = 9

=>x = 3cm

Hence length of the side of square is 3cm.

Now, we know that =>

Volume =
$(side) {3}$

=>Volume =

${3}^{3}$

=> Volume =27cm^3.

Hence the volume of the cube will be 27cm^3.

Remember

1)All Sides of square are equal.
2)The diagonal are equal and bisect each other at right angles.
3)Perimeter of square =4×(side)
4)Area of square = (side)^2
5)Volume of square =(side) ^3