Question

The sum of the lengths of the edges of a cube is equal to half the perimeter of a square. If the numerical value of the volume of the cube is equal to one-sixth of the numerical value of the area of the square, then the length of one side of the square is:

• A. 31.5 units
• B. 36 units
• C. 18 units
• D. 27 units

Answer 1

Answer:

B. 36 units

Let ‘a’ units be the side of the square.

So, perimeter of the square = 4a

Sum of the lengths of the edges of a cube = $12 \times$ length of one edge of a cube

⇒ 12 $\times$ length of one edge of a cube = $\frac{1}{2}\times{4a}=2a$

⇒ length of one edge of a cube = $\frac{2a}{12}=\frac{a}{6}$

Given, volume of the cube = one-sixth of the area of the square

⇒ $(\frac{a}{6})^2=\frac{1}{6}\times{a^2}$

$⇒\frac{a^3}{216}=\frac{a^2}{6}$

⇒ a = 36 units

∴ The length of one side of the square is 36 units.