The surface area of a cuboid is 3328 m square. If its dimensions are in the ratio 4:3:2 find the volume of cuboid
Answers
Given :-
Total Surface Area of cuboid = 3328 m²
The ratio of the dimensions are in ratio 4:3:2
To be found :-
The volume of the cuboid
Let
length be 4x m
breadth be 3x m
height be 2x m
We know that,
Total Surface Area of cuboid = 2(lb+bh+hl) unit sq.
[ ∴ In which l is the length, b is the breadth and h is the height of the cuboid ]
⇒ 3328 = 2(lb + bh + hl)
⇒ 3328 = 2(4x*3x + 3x*2x + 2x*4x)
⇒ 3328 = 2(12x² + 6x² + 8x²)
⇒ 3328 = 2(26x²)
⇒ 3328 = 52x²
⇒ 3328 ÷ 52 = x²
⇒ 64 = x²
⇒ √64 = x
⇒ 8 = x
∴ The value of x is 8
So,
length of the cuboid = 4x = 4*8 = 32 m
breadth of the cuboid = 3x = 3*8 = 24 m
height of the cuboid = 2x = 2*8 = 16 m
Now,
The volume of the cuboid = lbh unit cube
[ ∴ In which l is the length, b is the breadth and h is the height of the cuboid ]
= 32*24*16
= 12288 m³
Hence
the volume of the cuboid is 12288 m³
Answer:
Step-by-step explanation:
