The total area of the four vertical walls of a cuboid (its lateral surface area) is 448 sq cm. If the length of the cuboid is 18 cm and its height is 8 cm, what is its breadth in centimetres?

Introduction / Context:
This problem uses the concept of lateral surface area of a cuboid, which is the total area of its four vertical walls without counting the top and bottom faces. These questions simulate real life scenarios such as painting walls or putting wallpaper, where only the side surfaces matter. Given the lateral area, length, and height, we need to find the missing breadth of the cuboid.

Given Data / Assumptions:

• The figure is a cuboid with length, breadth, and height.
• The total area of the four walls (lateral surface area) is 448 sq cm.
• Length l = 18 cm.
• Height h = 8 cm.
• We are asked to find the breadth b in centimetres.

Concept / Approach:
The lateral surface area of a cuboid is given by the formula LSA = 2 * h * (l + b), because there are two walls of size l by h and two walls of size b by h. Using this formula, we can substitute the known values of LSA, l, and h, and then solve the resulting linear equation for b. Once we find b, we can quickly check whether it fits the original lateral surface area when substituted back into the formula.

Step-by-Step Solution:
Given LSA = 448 sq cm, l = 18 cm, and h = 8 cm.Formula: LSA = 2 * h * (l + b).Substitute: 448 = 2 * 8 * (18 + b).Compute 2 * 8 = 16, so 448 = 16 * (18 + b).Divide both sides by 16: 18 + b = 448 / 16 = 28.Therefore, b = 28 − 18 = 10 cm.

Verification / Alternative check:
To verify, recompute the lateral surface area using l = 18 cm, b = 10 cm, and h = 8 cm. LSA = 2 * h * (l + b) = 2 * 8 * (18 + 10) = 16 * 28 = 448 sq cm, which matches the given value exactly. This confirms that the breadth 10 cm is correct and consistent with the problem conditions.

Why Other Options Are Wrong:
Option 9 would give l + b = 27 and LSA = 2 * 8 * 27 = 432 sq cm, which is too small. Option 8 produces LSA = 2 * 8 * 26 = 416 sq cm, still not 448. Option 7 leads to LSA = 2 * 8 * 25 = 400 sq cm, and option 12 gives LSA = 2 * 8 * 30 = 480 sq cm, which is larger than required. Only b = 10 cm yields the correct lateral surface area of 448 sq cm.

Common Pitfalls:
Students sometimes confuse lateral surface area with total surface area and mistakenly use the formula 2(lb + bh + hl). Others may forget the factor of 2 when counting both pairs of opposite walls, or they might mix up the roles of height and breadth. Setting up the correct formula at the start and substituting values carefully helps avoid these errors.

Final Answer:
The breadth of the cuboid is 10 cm.