Given :

• Length of the CUBOID = 15 cm
• BREADTH of the cuboid = 12 cm
• Height of the cuboid = 10 cm

To find :

• Surface area of the cuboid
• Lateral surface area of the cuboid
• Length of the diagonal

Solution :

Surface area of the cuboid :-

Formula to calculate surface area of the cuboid :-

• Surface area of cuboid = 2(lb + bh + hl)

where,

• l denotes the length of the cuboid
• b denotes the breadth of the cuboid
• h denotes the height of the cuboid

Substituting the given values, we GET :-

→ Surface area = 2(15 × 12 + 12 × 10 + 10 × 15)

→ Surface area = 2(180 + 120 + 150)

→ Surface area = 2(450)

→ Surface area = 900

★ Surface area of the cuboid = 900 cm²

Lateral surface area of the cuboid :-

Formula to calculate lateral surface area of the cuboid :-

• Lateral surface area = 2h(l + b)

Substituting the given values, we get :-

→ Lateral surface area = 2 × 10(15 + 12)

→ Lateral surface area = 20(27)

→ Lateral surface area = 540

★ Lateral surface area of the cuboid = 540 cm²

Length of the diagonal :-

Formula to calculate length of diagonal of cuboid :-

• Length of diagonal = √(l² + b² + h²)

Substituting the given values, we get :-

→ Length of diagonal = √(15)² + (12)² + (10)²)

→ Length of diagonal = √(225 + 144 + 100)

→ Length of diagonal = √469

→ Length of diagonal = ± 21.65

As we KNOW, length of diagonal cannot be in negative. So, the negative sign will get rejected.

→ Length of diagonal = ± 21.65 Reject - ve

→ Length of diagonal = 21.65

★ Length of the diagonal of cuboid = 21.65 cm