Question

The length, breadth and height of cuboid
are in the ratio 3: 2:1. Its T.S.A is 550 cm3 then the volume is​

Answer 1

Step-by-step explanation:

let be X, 2x and 3x

T S A =550 cm

TSA of cuboid =2(lb+bh+lh)

550 = 2(2X ka square+class 6 ka square ++ 3 X ka square )

550 =2(11x square )

550=22 x ka square

x square = 550/22

X = 25 ka under root

X =5cm

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\therefore{\text{Dimension\:of\:cuboid=15\:cm,10\:cm,5\:cm}}}$

$\green{\therefore{\text{Volume\:of\:cuboid=750\:cm}^{3}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{given : }} \\ : \implies \text{Length(l) = 3x \: cm} \\ \\ : \implies \text{Breadth(b) = 2x\: cm} \\ \\ : \implies \text{Height(h) = x \: cm} \\ \\ :\implies \text{T.S.A\:of\:cuboid=550 cm}^{2} \\ \\ \red{ \underline \bold{to \: find : }} \\ : \implies \text{Dimensions \: of \: cuboid = ? }\\\\ :\implies \text{Volume\:of\:cuboid=?}$

• According to given question :

$\bold{As \: we \: know \: that} \\ : \implies \text{T.S.A \: of \: cuboid} = 2(lb + bh + hl) \\ \\ : \implies 550 = 2(3x \times 2x + 2x \times x + x\times 3x) \\ \\ : \implies 550= 2(6x^{2} + 2x^{2} + 3x^{2}) \\ \\ : \implies 550 = 22x^{2} \\\\ :\implies x=\sqrt{25} \\ \\ \green{: \implies \text{x=5 \:{cm}}^{2} }$

$\bold{Dimension} \\ \green{ : \implies \text{Length = 15\: cm}} \\ \\ \green{ : \implies \text{Breadth = 10 \: cm}} \\ \\ \green{ : \implies \text{Height = 5 \: cm}} \\ \\ \bold{As \: we \: know \: that} \\ : \implies \text{Volume \: of \: cuboid =} l\times b\times h \\ \\ \implies \text{Volume \: of \: cuboid =}15\times 10\times5\\ \\ \green{: \implies \text{Volume\: of \: cuboid =}750{cm}^{3} }$