Question

The length breadth and height of a cuboid are in the ratio of 3 : 3 : 4. Find its volume in m³ if its diagonal is `5sqrt(34)"cm"`.

Answer 1

Given that:
Diagonal of cuboid = `5sqrt(34)"cm"` ..................................(1)
Ratio of Length, breadth & height = 3 : 3 : 4
∴ Length (l) = 3x
Breadth (b) = 3x   &
Height (h) = 4x
We know that:-
Diagonal of cuboid
= `sqrt("l"^2 + "b"^2 + "h"^2`
= `sqrt((3x)^2 + (3x)^2 + (4x)^2)`
= `sqrt(9x^2 + 9x^2 + 16x^2)`
= `sqrt(34x^2)`
= `xsqrt(34)`
Also, 
`xsqrt(34) = 5sqrt(34)`   ...[From (1)]

i.e.,  x = `5sqrt(34)/(sqrt(34)`
∴ x = 5cm
Thus, 
Length = 3 x 5 = 15cm
Breadth = 3 x 5 = 15cm
Height = 4 x 5 = 20cm
∴ Volume of cuboid
= l x b x h
= 15 x 15 x 20
= 225 x 20
= 4500cm³
= 0.0045m³ .    ...[∵ 1m³ = 10⁶cm³]