Question

The edges of a cubold are In the ratio 1 : 2 : 3 and its surface area is 88 cm2. The volume of the cubold is

(a) $48c{m}^3$

(b) $64c{m}^3$

(c) $96c{m}^3$

(d) $120c{m}^3$

Answer 1

Ratio in sides of cuboid =1 : 2 : 3

Surface area $=88c{m}^2$

Let l =x, b =2x and h =3x

Then 2(lb+bh +hl)=88

$\Rightarrow 2(2x^2+6x^2+3x^2)=88$

$\Rightarrow 2\times 11x^2=88$

$\Rightarrow x^2=\frac{88}{22}=4=(2{)}^2$

$\Rightarrow x=2$

$\Rightarrow l=2cm,b=2x=2\times 2=4cm$

and $h=3x=3\times 2=6cm$

Now volume $=l.b.h=2\times 4\times 6c{m}^3$

$=48c{m}^3$