diagonal of a cube is root of 27 what is it's volume and surface area
Answers
Answer :-
27 cu.units and 54 sq units
Solution :-
Diagonal of the cube = √27 units
Let the side of the cube be 'a' units
Let 'd' be the diagonal of the base of cuboid
Consider the Right triangle formed by diagonal and 2 sides
By Pythagoras theorem
⇒ d² = a² + a²
⇒ d² = 2a²
⇒ d = √2 * a
So, Diagonal of the base of cube = √2 * a units
Consider the Right triangle formed by diagonal of cube, diagonal of cuboid and side of cube
By pythagoras theorem
⇒ ( √27 )² = a² + ( √2 * a)²
⇒ 27 = a² + 2a²
⇒ 27 = 3a²
⇒ 27/3 = a²
⇒ 9 = a²
⇒ a = √9 = ± 3
Sides cannot be negative
⇒ a = 3
Hence, side of the cube is 3 units
Volume of the cube = a³ cu.units = 3³ = 27 cu.units
Surface area of the cube = 6a² sq.units = 6 * 3² = 6 * 9 = 54 sq.units
Therefore Volume is 27 cu.units and surface area is 54 sq.units.