Question

the surface area of a cuboid is 4212m^2.If its dimension are in the ratio 4:3:2, find the volume of the cuboid.​

Answer 1

let the dimensions be 4x,3x,2x

volume of cuboid- length× breadth× height

surface area of cuboid= 2(lb+lh+bh)

4212m²= 2(4x×3x+ 4x×2x+ 3x×2x)

4212= 2(12x²+ 8x²+ 6x²)

4212= 24x²+16x²+12x²

4212= 52x²

4212/52=x²

81=x²

9m=x

therefore the value of x is 234

4x= 9×4=36

3×= 9×3=27

2x=9×2=18

volume of cuboid= length×breadth×height

36×27×18

17496

therefore the volume of cuboid

is 17496m³