Answer:
a) [tex]2.036x^-\frac{1}{3}[/tex]
b) [tex]\frac{x^2}{\sqrt{x+1} }[/tex]
Step-by-step explanation:
For a cube, all the sides are equal. Let the length of each side be L
a) The volume of a cube (V) = L³
For the first cube:
V = 270x in³
270x = L³
L = ∛(270x) = [tex]6.463x^\frac{1}{3}[/tex]
For the second cube:
V = 32x² in³
32x² = L³
L = ∛(32x²) = [tex]3.175x^\frac{2}{3}[/tex]
Ratio of length = [tex]\frac{6.463x^\frac{1}{3} }{3.175x^\frac{2}{3} }=2.036x^-\frac{1}{3}[/tex]
b) The surface area of a cube (s) = 6L²
For the first cube:
s = 6x⁴ ft²
6x⁴ = L²
L = √6x⁴= 2.45x²
For the second cube:
s = 6(x + 1) ft²
6(x + 1) = L²
L = √6(x + 1)= 2.45√(x + 1)
Ratio of the length = [tex]\frac{2.45x^2}{2.45\sqrt{ (x + 1)}} =\frac{x^2}{\sqrt{x+1} }[/tex]
