Surface Area of a Cuboid: Solving for X When Surface Area = 862 cm²

To solve this problem, we'll calculate the surface area of the cuboid and solve for the unknown dimension $X$ using the formula for the surface area of a cuboid.

Given dimensions are:

• Length: $20 - X$
• Width: $11 \, \text{cm}$
• Height: $13 \, \text{cm}$

Using the formula for the surface area of a cuboid: $SA = 2(lw + lh + wh)$ Substitute the values: $862 = 2((20-X) \times 11 + (20-X) \times 13 + 11 \times 13)$

First, simplify the more straightforward terms: $11 \times 13 = 143$ Next, distribute and simplify: $(20-X) \times 11 = 220 - 11X$ $(20-X) \times 13 = 260 - 13X$ $SA = 2((220 - 11X) + (260 - 13X) + 143)$ $SA = 2(623 - 24X)$

Set this equation equal to the surface area: $862 = 2(623 - 24X)$ $862 = 1246 - 48X$ Rearranging gives: $48X = 1246 - 862$ $48X = 384$ Solving for $X$: $X = \frac{384}{48} = 8$

Therefore, the value of $X$ is 8 cm.