Question

The surface area of cuboid is 1372 sq.cm. If its dimensions are in ratio 4:2:1,find its volume.

Answer 1

let the dimensions be 4x 2x and x
so according to the formula for the TSA of a cuboid
2(lb+bh+lh)= 1372
2*((4x*2x)+(2x*x)+(4x*x))=1372
2*(8x^2+2x^2+4x^2)=1372
2*14x^2=1372
28x^2=1372
x^2=1372/28
x^2=49
x=√49
x=7
4x=4*7=28
2x=2*7=14
volume=l*b*h
14*28*7
so the volume is
2744 with the respective unit

it is to the power.

Answer 2

Answer:

Volume = 2744 m³

Step-by-step explanation:

The surface area of the cuboid= 1372 sq. cm 

  Let the dimensions =4x, 2x, 1x

     The total surface area of the cuboid

= 2(lb+bh+hl) = 1372

                  = 2(4x × 2x + 2x × 1x + 4x × 1x ) =1 372 

= 2(8x²+2x²+4x²) = 1372

= 2(14x²) = 1372

= 28x² = 1372

x² = 1372/28

        x² = 49

x = 7 m

So, the dimensions are

Length - 4x = 4×7 = 28m

                    Breadth  -  2x = 2×7 = 14m

                    Height  -   1x = 1×7 = 7m

So, the volume of the cuboid = l × b × h

= 28 × 14 × 7

= 2744 m³

Answer : Volume = 2744 m³