length of diagonal of a cube is 3√3 cm then its volume is
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Verified answer
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 =
⇒ 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.
Verified answer
Given,length of diagonal of square =
=
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 =
=>2x^2 = 9 ×2
=> x^2 = 9
=>x = 3cm
Hence length of the side of square is 3cm.
Now, we know that =>
Volume =
=>Volume =
=> 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