Question

The surface area S of a cube is equal to the sum of the areas of the 6 square faces that form the cube. We want to paint the cube and need to know how many square units of paint to purchase. If each face has side length s, then the formula S = 6s2 can be used to find the surface area of the cube. The length of a side is indicated in the cube below( s = x - 5). The surface area of the cube is 1944 units2. What is the value of x? SHOW and EXPLAIN each of the steps you used to solve.

Answer 1

Answer: x equals 23

Step-by-step explanation: The information available to us is as follows;

Surface area of the cube = 1944

Side length of the cube = x - 5

Note however that the surface area is also derived as S = 6s²

In order to calculate the value of s we would start by substituting for the known values as follows;

S = 6s²

1944 = 6[(x - 5)²

1944 = 6[(x² - 10x + 25)]

By cross multiplication we now have

1944/6 = (x² - 10x + 25)

324 = x² - 10x + 25

Collect like terms and we now have;

x² - 10x -299 = 0

By factorization we now have;

(x - 23) (x + 13) = 0

Therefore, x - 23 = 0 and hence x = 23

OR

x + 13 = 0 and hence x = -13

Knowing that the length of the side is not a negative number, we would choose x = 23.

**(Having been given that x = 23,

s = x - 5

s = 23 - 5

s = 18)**