Surface Area 752 cm²: Find X in Cuboid Dimensions (12cm × 8cm × (X+4))

Question

Look at the cuboid in the figure below.

Its surface area 752 cm².

Calculate X.

00:00 Find X

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

00:08 We'll substitute appropriate values according to the given data and solve for X

00:27 We'll simplify what we can

00:46 We'll group like terms

00:55 We'll isolate the unknown X

01:09 And this is the solution to the problem

The surface area formula for a cuboid is given by:

$SA = 2(lw + lh + wh)$

Substitute the given dimensions and surface area into this formula:

$752 = 2(12 \times 8 + 12 \times (X + 4) + 8 \times (X + 4))$

First, calculate each product:

Substitute these products back into the equation:

$752 = 2(96 + 12X + 48 + 8X + 32)$

Combine like terms inside the parentheses:

$752 = 2(176 + 20X)$

Distribute the 2:

$752 = 352 + 40X$

Isolate $X$ by subtracting 352 from both sides:

$400 = 40X$

Divide by 40:

$X = 10$

Thus, the value of $X$ is 10 cm.

10 cm