Question

Length breadth and height of a rectangular solid are in the ratio 5 ratio 4 ratio 2 if its total surface area is 1216 cm cube find the volume of the solid

Answer 1

here, ratio is 5:4:2
let the length be 5x, breadth be 4x and height be 2x
so,
TSA of cuboid = 2(lb+bh+hl)
1216 = 2(5x*4x+4x*2x+2x*5x)
608 = 20x²+8x²+10x²
608 = 38x²
x² = 608/38
x² = 16
x = √16
x = 4
so,
length = 5×4 = 20 cm
breadth = 4×4 = 16 cm
height = 2×4 = 8 cm
hence,
volume = lbh = 20×16×8 = 2560 cm³.

Answer 2

Let x be the common factor.
length = 5x, breadth = 4x, height = 2x
Total Surface Area = 1216sq.cm
2(lb + lh+ bh)= 1216
2( 5x×4x+ 5x×2x +4x×2x)= 1216
2(20x+10x+8x) = 1216
2× 38x=1216
x= 1216/2×38
x=16
length=80cm. breadth= 64cm.
height = 32cm.
Volume of the solid = 80×64×32
=163840 cu.cm