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 _______.
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