Question

the square of diagonal of a cube is 675 sq cm . find the volume of cube

Answer 1

let 'a' be the side of the cube.
diagonal of the cube=  √3a^2
 by data,
square of diagonal of cube is 675 sq cm
3a^2= 675
a^2= 675/3
a^2= 225
a= 15
volume of a cube= a^3
volume of a cube= (15)^3
                         = 3375 cm^3
therefore,volume of the cube is 3375 cm^3

Answer 2

let the side of cube = s
diagonal = $\sqrt{3}\ s$

given that square of diagonal = 675
⇒3s² = 675
⇒ s² = 675/3 = 225
⇒ s = √225 = 15 cm

volume = s³ = 15³ cm³ = 3375 cm³