The breadth of a cuboid is 2 less than its length and it's height is one less than its breadth. If the surface area of cuboid is 188m²,find its volume.
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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 ..
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Answer:
Step-by-step explanation:
Let the length be l.
Breadth = l - 2
Height = l - 2 - 1 = l - 3
SURFACE AREA :
2 × l × (l - 2) = 2l^2 - 4l
2 × l × (l - 3) = 2l^2 - 6l
2 × (l - 2)(l - 3) = 2(l^2 - 5l + 6) = 2l^2 - 10l + 12
We add these as follows :
2l^2 - 4l + 2l^2 - 6l + 2l^2 - 10l + 12
6l^2 - 20l + 12 = 188
6l^2 - 20l - 176 = 0
Divide through by 2:
3l^2 - 10l - 88 = 0
The roots are : - 22 and 12
3l^2 + 12l - 22l - 88 = 0
3l(l + 4) - 22(l + 4) = 0
(3l - 22)(l + 4) = 0
3l = 22
l = 22/3 m
or l = - 4
We take the positive value.
l = 22/3
Breadth = 22/3 - 2 = 16/3
Height = 22/3 - 3 = 15/3
Volume = length × width × height
22/3 × 16 /3 × 15/3 = 1760/9 m ^3
= 195.555 m cubed.
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