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Maths-

General

Easy

Question

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

hint Hint:

Area of square=side × side=a²
Diagonal of cube= $square root of 3 cross times side equals square root of 3 a$ unit

The correct answer is: 155 cm.

The length of the square and the diagonal of the cube are coincided. Therefore, the value of the two will be equal.

We are given that,

Area of the square=72,075 cm²
Side of square=Diagonal of cube
Let the edge of the cube be 'a' cm.
As we know,
length of the diagonal of cube= $square root of 3$ ×edge of the cube= $square root of 3$ a cm

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)

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals left parenthesis square root of 3 a right parenthesis squared cm squared end cell row cell equals 3 a squared cm squared end cell end table$

We know that, area of square drawn on the diagonal of a cube= 72,075 cm²

Therefore,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 3 a squared equals 72075 cm squared end cell row cell => a squared equals 72075 over 3 end cell row cell => a squared equals 24025 end cell row cell => a equals square root of 24025 end cell row cell => a equals 155 cm end cell end table$

Therefore , the side of the cube is 155 cm.

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