The length and breadth of a cuboid are 15 cm and 8 cm respectively. If the volume of the cuboid is 1560 cm$^3$, calculate the total surface area.

Step 1: Analyze the question We have a cuboid with length l = 15 cm, breadth b = 8 cm and volume V = 1560 cm³. We must find the height first, then the total surface area.

Step 2: Concept

• Volume = l × b × h
• Total surface area = 2(lb + lh + bh)

Step 3: Solution

Find the height: 15 × 8 × h = 1560 120h = 1560 h = 13 cm

Now the surface area:

• lb = 15 × 8 = 120
• lh = 15 × 13 = 195
• bh = 8 × 13 = 104

Sum = 120 + 195 + 104 = 419

Total surface area = 2 × 419 = 838 cm²

Step 4: Answer

Tip: In cuboid problems, always find the missing dimension from the volume first. Then use 2(lb + lh + bh) and add the three pair-areas before doubling, which helps avoid arithmetic slips. Also, 120 × 13 = 1560 is a quick check on h.