Question

The square on the diagonal of a cube has an area of 441 cm². Find the length of the side and total surface area of the cube.

Answer 1

Area of a Square = 441cm²
side² = 441
side = `sqrt(441)`
∴ side = 21cm
∴ The length of the diagonals of the cube is 21cm.
Let 'a' be the side of the cube
Diagonal of a cube = `sqrt(3) xx "a"`
∴ 21 = `sqrt(3) xx "a"`

a = `(21)/sqrt(3)`

a = `(21)/sqrt(3) xx sqrt(3)/sqrt(3)`
(rationalising the denominator)

a = `(21sqrt(3))/(3)`
a = `7sqrt(3)"cm"`
Total surface area of a cube 
= 6a²
= 6 x `(7sqrt(3))^2`
= 6 x 49 x 3
= 882cm²
∴ Side of the cube is `7sqrt(3)"cm"` and the total surface area of the cube is 882cm².