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Question

If a brick has length, breadth and height in the ratio 1:2:3 and the total surface area of the brick is 792 sq. m, then the volume of the brick is _______.


A

1296 m3

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B

1396 m3

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C

1496 m3

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D

1596 m3

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Solution

The correct option is A

1296 m3


Given,
length(l) : breadth(b) : height(h) = 1:2:3
Total surface area = 792 sq. m

Let the length be x units.
Then, b=2x units and h=3x units

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

2(lb+bh+hl)=792

2(2x2+6x2+3x2)=792

22x2=792

x2 = 79222=36

x=6 m
(Since x is the length and length is always positive.)

l=6 m, b=12 m, h=18 m

Hence, volume = lbh
= 6×12×18
= 1296 m3


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