Question

If the area of the adjacent faces of a cuboid are in ratio 2:3:4 and its volume is ${\sf {9000\: {c.m.}^{3}}}$ . Find its sides.​

Answer 1

${\huge{\underline{\underline{\rm{Question:-}}}}}$

Q) If the Area of the adjacent faces of a Cuboid are in the ratio 2 : 3 : 4 and its volume is 9000 cm³ . Find its sides

${\huge{\underline{\underline{\rm{Answer\checkmark}}}}}$

☆ Given :

• Ratio of areas of adjacent faces = 2:3:4
• Volume = 9000 cm³

☆ To Find :

• Length , breadth and height .

☆ Solution :

• Let length be l
• breadth be b
• Height be h

We have ,

Ratio of areas of adjacent faces = 2 : 3 : 4

$\mapsto \rm \: bh: lh : lb= 2 : 3 : 4$

let the ratios be 2x , 3x and 3x

• bh = 2x
• lh = 3x
• lb = 4x

Multiply this all

$\mapsto \rm \: bh \times lh \times lb = 2x \times 3x \times 4x$

$\mapsto \rm \: {(lbh)}^{2} = 24 {x}^{3}$

As we know ,

$\boxed{ \sf \: volume = lbh = 9000 \: {cm}^{3} }$

put it above .

$\mapsto \rm \: {9000}^{2} = 24 {x}^{3}$

$\mapsto \rm \: \cancel{9000} \times 9000 = \cancel{24} {x}^{3}$

$\mapsto \rm \: {x}^{3} = 375 \times 9000$

$\mapsto \rm \: x = \sqrt[3]{3375000}$

$\mapsto \rm \: x = 150$

Now , finding the sides ...

We have -

• bh = 2x
• lh = 3x
• lb = 4x

So ,

$\sf \: \frac{ \cancel{b}h}{l \cancel{b}} = \frac{2}{4}$

$\mapsto \sf \: \frac{h}{l} = \frac{1}{2}$

$\mapsto \boxed{\rm \: l = 2h}$

We know that ,

$\rm \: lh =3x$

$\mapsto \rm \: \cancel2h \times h = 3 \times \cancel{150}$

$\mapsto \rm \: {h}^{2} = 3 \times 75$

$\mapsto \rm \: h = \sqrt{225}$

$\mapsto \pink{\underline{ \boxed{ \rm \: h = 15\: cm}}}$

And

$\mapsto \rm \: l = 2h$

$\mapsto \rm \: l = 2 \times 15 \: cm$

$\mapsto \orange{ \underline{ \boxed{ \rm \: l = 30 \: cm \: }}}$

Now ,

$\mapsto \rm \: bh = 2x$

$\mapsto \rm \: b \times \cancel{15 }= 2 \times \cancel{150}$

$\mapsto \purple{ \underline{ \boxed{ \rm \: b = 20 \: cm \: }}}$

_________________________

So , the sides of the Cuboid would be :

• Length = 30 cm
• Breadth = 20 cm
• Height = 15 cm

★ Note : The value of breadth and height can be interchanged .

Answer 2

Answer:

well you already got the answer