The breadth of a cuboid is $$\frac{2}{3}$$ of its length and its height is $$\frac{3}{4}$$ of its breadth. If its volume is 72 cu.mts, then its surface area. in sq.mts, is

As per given question,

volume of cuboid=72 cu. mts

Let the length of the cuboid be$$=x$$

breadth$$=\dfrac{2}{3}\times x$$

then height$$=\dfrac{3}{4}\times \dfrac{2}{3}\times x$$

as we know volume of cuboid$$= length \times breadth \times height$$

$$\Rightarrow x\times \dfrac{2}{3}\times x \dfrac{1}{2} \times x$$

$$\dfrac{1}{3}\times x^3=72$$

$$x^3=216$$

x=6

then length=6

breadth$$=\dfrac{2}{3}\times 6=4$$

height$$=\dfrac{3}{4}\times \dfrac{2}{3} \times 6=3 $$

as we know suface area of cuboid$$=2(lb+bh+hl)$$

surface area$$=2(6\times 4+4\times 3+3\times 6) $$

surface area= 108 sq.mts