The dimensions of a cuboid are 15cm 12cm and 10cm then find i ) surface area ii)lateral surface area iii)length of diagonal
Answers
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