Question

A square is drawn with the length of side equal to the diagonal of a cube. If the area of the square is 72075 cm², then find the side of the cube.​

Answer 1

✤$\textsf{\large{\underline{Question}:-}}$

A square is drawn with the length of side equal to the diagonal of a cube. If the area of the square is 72,075 cm², then find the side of the cube.

✤$\textsf{\large{\underline{Important Formulas}:-}}$

• Area of square=side×side=a²
• Diagonal of cube=√3×side=√3a unit

✤$\textsf{\large{\underline{Solution}:-}}$

☆Refer to the attachment for clear understanding of the question.The length of the square and the diagonal of the cube are coincided.Therefore,the value of the two will be equal.

✤$\textsf{\large{\underline{Given}:-}}$

Area of the square=72,075 cm²

Side of square=Diagonal of cube

$\textbf{Now:-}$

Let the edge of the cube be 'a' cm.

As we know,length of the diagonal of cube=

√3×edge of the cube=√3a cm

✤$\textsf{\large{\underline{A/Q}:-}}$

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

Area of square(drawn on diagonal of cube)

$= {( \sqrt{3a)} } \: ^{2} \: {cm}^{2}$

$= 3 {a}^{2} \: {cm}^{2}$

$\textbf{Substituting the values:-}$

• Area of square drawn on the diagonal of a cube= 72,075 cm²

Therefore,

$= > 3 {a}^{2} = 72075 \: {cm}^{2}$

$= > {a}^{2} = \frac{72075}{3} \:$

$= > {a}^{2} = 24025 \:$

$= > a = \sqrt{24025}$

$= > a = 155 \: cm$

✤$\textsf{\large{\underline{Answer}:-}}$

Therefore,the side of the cube is 155 cm.