Question

PLEASE HELP!!

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

x = 23

Explanation:

6s² = 1944

Total area is given to be 1944

Since s = x - 5,

6(x - 5)² = 1944

Divide both sides by 6

(x - 5)² = 324

Square root both sides

x - 5 = +/- 18

Solve for x

x = 18 + 5 = 23

x = -18 + 5 = -13 (not possible because lengths can't be negative)

So, x = 23

Answer 2

x = 23

Explanation:

We know that the surface area of a cube is denoted by S = 6s². In this case, we see that s = x - 5, so just plug x - 5 in for s in the formula:

S = 6(x - 5)²

We also know that the surface area is 1944, so S = 1944. Plug this in as well:

S = 6(x - 5)²

1944 = 6(x - 5)²

Now, we solve by expanding the right:

1944 = 6(x² - 10x + 25) = 6x² - 60x + 150

Subtract 1944 from both sides:

6x² - 60x - 1794 = 0

Divide by 6 from both sides for simplicity:

x² - 10x - 299 = 0

Factor:

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

x = 23 or x = -13

Obviously, we can't have a negative length, so -13 is wrong. We use x = 23 instead.

The answer is thus x = 23.