Question

The square on the diagonal of a cube has an area of 1875cm2.calculate the side of a cube

Answer 1

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Find Side of  the Square

Let the Side of the Square be  "x "

Let the side of the Cube be " a "

We have given the area of Square = 1875 cm^2

s^2 = 1875 cm^2

s = $\sqrt{1875} cm^2$

s => $25\sqrt{3}$

Find the Side of the Cube

Side of Square = diagonal of the Cube

diagonal of cube = √(3a²)

$\sqrt{3} * a = \sqrt[25]{3}$

=> a = 25 cm

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Answer 2

$\bold \blue{here \: is \: your \: answer}$


Let the edge of the cube be a cm.


We know that, length of diagonal of the cube =

∴ Length of diagonal of the cube = a cm


The side of the square is equal to the length of diagonal of the cube.

Area of square drawn on the diagonal of the cube = = 3a2 cm2 [Area of the square = (side)2]


therefore, 3a2 = 1875cm2 (Given)

=> a2 = 625cm2 = (25cm)2

=> a = 25cm

Edge of the cube = a = 25cm

Total surface area of the cube = 6a2 = 6 × (25cm)x2
= 5 × 625cm2
= 3750 cm2