RRB Group D 15-Sep-2018 Shift 1 Solved Paper

Question : 36 of 100

Marks: +1, -0

The sum of the lengths of the edge of a cube is equal to three-fifths of the perimeter of a square. If the numerical value of the volume of the cube is equal to the numerical value of the area of the square, then the perimeter of the square is :

360 units
500 units
480 units
300 units

Validate

Solution:

Let edge of the cube

=a

units
Side of the square

=s

units
From the question,

12 a=\;{3}/{5}[4 s]

⇒ \;\; s=\;{12 × 5 × a}/{3 × 4}=5 a

Also,

a^{3}=s^{2}

∴ \;\; a^{3}=(5 a)^{2}

a^{3}=25 a^{2}

\;\; a^{2}(a-25)=0

⇒ \;\; a=25

Thus, perimeter of the square

=4 × 5 × 25

=20 × 25=500

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