if length, breath and height of a cuboid are in ratio 5:3.2 find volume if its total Surface area is 279cm²
Answers
Step-by-step explanation:
ratio of length,breadth and height of a cuboid = 5:3:2
Total surface area = 279cm²
Formula of total surface area of a cuboid = 2(lb+bh+lh)
Here,l = length
b = breadth
h = height
2(lb+bh+lh) = 279cm²
lb+bh+lh = 279/2cm²
lb+bh+lh = 139.5cm²
let the number be x
then,length = 5x
breadth = 3x
height = 2x
5x×3x+3x×2x+5x×2x = 139.5cm²
15x²+6x²+10x² = 139.5cm²
31x² = 139.5cm²
x² = 139.5/31cm²
x² = 4.5cm²
x = root over 4.5cm²
x = 2.12cm
length = 5x = 5×2.12 = 10.6
breadth = 3x = 3×2.12 = 6.36
height = 2x = 2×2.12 = 4.24
Formula of volume of a cuboid = lbh = l×b×h
Volume of a cuboid = 10.6×6.36×4.24
= 285.84
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Given :
→ Ratio of the length, breadth and height of the cuboid = 5 : 3 : 2
→ Total surface area of cuboid = 279 cm²
To find :
→ Volume of the cuboid
Solution :
Let,
- The length of the cuboid = 5x
- The breadth of the cuboid = 3x
- The height of the cuboid = 2x
Using formula,
→ Surface area of cuboid = 2(lb + bh + hl)
where,
- l = length
- b = breadth
- h = height
Substituting the given values :-
→ 279 = 2(5x × 3x + 3x × 2x + 2x × 5x)
→ 279 = 2(15x² + 6x² + 10x²)
→ 279 = 2(31x²)
→ 279 = 62x²
→ 279 ÷ 62 = x²
→ 4.5 = x²
→ Taking square root on both the sides :-
→ √4.5 = x
→ √(2.12 × 2.12) = x
→ ± 2.12 = x
→ As we know, the side of cuboid cannot be negative. So, the negative sign will get rejected.
→ Therefore, the value of x = 2.12
Substitute the value of 'x' in the dimensions of the cuboid :-
→ Length = 5x = 5(2.12) = 10.6 cm
→ Breadth = 3x = 3(2.12) = 6.36 cm
→ Height = 2x = 2(2.12) = 4.24 cm
Using formula,
→ Volume of cuboid = l × b × h
Substituting the given values :-
→ Volume = 10.6 × 6.36 × 4.24
→ Volume = 285.84384
On rounding off, we get :-
→ Volume = 285.84
Therefore, volume of the cuboid = 285.84 cm³