The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. If its total surface area is `504 cm^(2)`, find its dimensions. Also find the volume of the cuboid.

Explanation

If length = 6x, breadth = 5x and height = 3x.
`therefore` Total surface area `= 2(lb+bh+hl)`
`therefore 504 = 2(6x xx5x + 5x xx 3x + 3x xx 6x)`
`rArr 504 = 2(30x^(2)+15x^(2)+18x^(2))`
`rArr 63x^(2)=252`
`rArr x^(2)=4`
or x = 2
Therefore, length `= 6xx2=12 cm`
breadth `=5xx2=10 cm`
and height `=3xx2=6 cm`
Now, volume of cuboid `= l xx b xx h`
`rArr` Volume `= 12xx10xx6`
`rArr` Volume `=720 cm^(3)`