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

√2

Step-by-step 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

x =
`\sqrt{(S)/(6) }` or
`( (S)/(6) )^{(1)/(2) }`

Step-by-step 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)` =
`(S)/(6)`

`x^(2)` =
`(S)/(6)`

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

`\sqrt{x^(2) }` =
`\sqrt{(S)/(6)}` ⇒ x =
`\sqrt{(S)/(6)}`

x =
`\sqrt{(S)/(6) }` or
`( (S)/(6) )^{(1)/(2) }`

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