Question

A company produces a cardboard box in the shape of a cube. The surface area of the box is represented by S=6x2, where x is the edge length of the box. Find the inverse by solving for x without switching the variables.

Answer 1

Answer:

√2

Explanation:

Before answering this question I must tell the following formulas:

Volume of Cube = S3  

Surface Area of Cube = 6S2  

If S = 6x2, then the value of x must be √2. In this way the original equation would have been S = 6 x (√2) 2 which would give the value S = 6x2.

Answer 2

Answer:

x = $\sqrt{\frac{S}{6} }$  or $( \frac{S}{6} )^{\frac{1}{2} }$

Explanation:

The cardboard box is in the shape of a cube. The surface area of the box is given by:

S = 6$x^{2}$

To find the inverse, we have to solve for x. To solve for x means we will make x the subject of the equation above

Divide both the right and left hand side by 6, we have:

6$x^{2}$ ÷ 6 = S ÷ 6 ⇒ $x^{2}$ = $\frac{S}{6}$

$x^{2}$ = $\frac{S}{6}$

Take the square root for both the right and left hand side, we have:

$\sqrt{x^{2} }$ = $\sqrt{\frac{S}{6}}$ ⇒ x =  $\sqrt{\frac{S}{6}}$

x = $\sqrt{\frac{S}{6} }$  or  $( \frac{S}{6} )^{\frac{1}{2} }$

Therefore, x is equivalent to the square root of (S/6)