Correct option is (B) x – 2
Let the side length of the cube be x units.
\(\therefore\) Volume of the cube \(=a^3\) cubic units.
But given that volume of the cube is \(x^3-6x^2+12x-8.\)
\(\therefore\) \(a^3=x^3-6x^2+12x-8\)
\(=x^3-2x^2-4x^2+8x+4x-8\)
\(=x^2(x-2)-4x(x-2)+4(x-2)\)
\(=(x-2)(x^2-4x+4)\)
\(=(x-2)(x-2)^2\)
\(=(x-2)^3\)
\(\Rightarrow\) a = (x - 2)...
Correct option is (B) 9 cm
Let the side of cube be a.
\(\therefore\) \(a^3=729=9^3\) \((\because\) Volume of cube \(=a^3)\)
\(\Rightarrow\) a = 9 cm
Hence, side of cube is 9 cm.
Correct option is (B) 64 cm3
Let side of cube is a.
\(\therefore6a^2=96\) \((\because\) Total surface area of cube \(=6a^2)\)
\(\Rightarrow a^2=\frac{96}6=16=4^2\)
\(\therefore\) a = 4 cm
Volume of cube \(=4^3=64\,cm^3\)
