Question

the dimensions of a cuboid are 4:2;1 and the total surface area is 2800 square.m find its volume

Answer 1

let the dimensions be 4x,2x,x
so by this total surface area is equal to (4x ×2x) + (2x × x ) + (4x × x )
⇒8x² + 2x² + 4x² = 2800 (given)
⇒14x² = 2800
⇒x² = 2800/14
⇒x² = 200
⇒x = √200 = 10√2
volume = 4x × 2x × x = 8x³
= 8×(10√2)³
=32000√2

Answer 2

Let x be a variable,
                             then,
Length=4x 
Breadth=2x
Height=x

Total Surface Area (TSA)=2800 m²

TSA=2(lb+bh+hl)
2800/2=4x*2x+2x*x+4x*x
1400=8x²+2x²+4x²
1400=14x²
1400/14=x²
100=x²
√100=x
10=x

therefore,length=4x=40 m
breadth=2x=20 m
height=x=10 m

volume=l*b*h
          =40*20*10
          =8000 m³