Surface Area of Cuboid = 18X + 7: Find the Unknown Dimension X

Question

The surface area of the cuboid is 18X + 7.

Calculate X.

00:00 Find X

00:03 We'll use the formula for calculating the surface area of a box

00:08 2 multiplied by (sum of face areas)

00:15 We'll substitute appropriate values and solve for X

00:52 We'll solve each multiplication separately and sum

01:06 We'll properly expand brackets, multiply by each factor

01:22 We'll isolate X

01:33 We got an illogical expression, therefore there's no solution to the question

To determine the value of $X$ , we'll use the formula for the surface area of a cuboid:

The formula for the surface area of a cuboid is $2(lw + lh + wh)$ .

Given that $l = 5$ , $w = 4$ , and $h = X$ , we plug these values into the surface area formula:

$2(5 \times 4 + 5 \times X + 4 \times X) = 2(20 + 5X + 4X) = 2(20 + 9X) = 40 + 18X$

We equate this expression to the given surface area:

$40 + 18X = 18X + 7$

By simplifying, we subtract $18X$ from both sides:

$40 = 7$

Which simplifies to a contradiction, demonstrating that these conditions are not possible with the given figure.

Conclusively, the given surface area is not possible.

The given surface area is not possible.