Question

the surface area of a cuboid is 1792 cm if its length , breadth and height are in the ratio 4:2:1 then find the length of the coboid

Answer 1

aloha!

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here is your answer

the total surface area of cuboid =2(lb + bh + hl)


now,


the ratio is 4:2:1

let the unknown value be n

length = 4n
breadth= 2n
height = n


putting them in the formula we get,

2(lb + bh + hl) = 1792
2(4n × 2n + 2n × n + n × 4n) =1792
2(8n^2 + 2^2 + 4n^2) =1792
2(14n^2)= 1792
n^2= 1792/2 × 14
n^2= 64
n= root 8 × 8
n=8cm


now

length =4n
= 4(8)
= 32 cm

breadth= 2n
= 2(8)
= 16 cm

height= n = 8cm


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hope it helps :^)

Answer 2

Surface area of cuboid = 2(LB + LH + BH)
Let the length ,breadth and height respectively be 4x ,2x and 1x
1792 = 2(4x × 2x + 2x × 1x + 1x × 4x)
1792 = 2(8x square + 2x square + 4x square)
1792 = 2(14x square)
1792 =28x square
1792/28 = x square
64 = x square
√64 = x
x = 8
Length = 4×8=32cm
Breadth=2× 8= 16cm
Height = 1 × 8= 8cm