Question

The Length, Breadth and Height of a cuboid are in the ratio 6:5:3. If it's total surface area is 504 cm^2, find it's dimensions. Also , find the volume of the cuboid.​

Answer 1

Answer:

total surface area is 504cm

2

The length, breadth, and height of a cuboid are in the ratio 6:5:3

total surface area =2(lb+bh+lh)

504 = 2(30x

2

+15x

2

+18x

2

)

504 = 2 x 63x

2

504 = 126x

2

x

2

=

126

504

= 4

∴x=2cm

Therefore,length= 6x=6x2 = 12cm

breadth = 5x =5(2) =10cm

height = 3x=3(2)=6cm

Volume of cuboid = area of the base x height = l×b×h = 12 x 10 x 6 = 720cm

Answer 2

Given:-

${ \rm \red{\bullet \: The \: length, \: breadth \: and \: height \: of \: a \: cuboid \: are \: in \: the \: ratio \: 6 \: : \: 5 \: : \: 3}}$

${ \rm \pink{\bullet \: Total \: Surface \: Area \: is \: 504 \: cm²}}$

To Find:-

${ \rm \purple{\bullet \: Dimensions \: of \: the \: cuboid}}$

${ \rm \green{\bullet \: Volume \: of \: the \: cuboid}}$

Solution:-

Let, the length, breadth and height of a cuboid be 6x, 5x and 3x

We know,

${ \bf \boxed {\rm \pink {Total \: Surface \: Area \; = \: 2(lb \: + \: bh \: + \: lh)}}}$

Therefore,

$\bf 504 \; = \: 2(6x \: × \: 5x \: + \: 5x \: × \: 3x \: + \: 6x \: × \: 3x)$

$\bf 504 \; = \: 2(30x² \: + 15x² \: + \: 18x²)$

$\bf 504 \; = \: 2 \: × \: 63x²$

$\bf 504 \; = \: 126x²$

$\bf x² \: =$ $\bf \frac {\cancel{504} \: \: 4}{\cancel{126}}$

$\bf x² \: = \: 4$

$\therefore$ $\bf x \: = \: 2 \: cm$

So, $\bf Length \: = \: 6x \: = \: 6 \: × \: 2 \: =$ ${ \bf {\rm \purple {12 \: cm}}}$

$\bf Breadth \: = \: 5x \: = \: 5 \: × \: 2 \: =$ ${ \bf {\rm \pink {10 \: cm}}}$

$\bf Height \: = \: 3x \: = \: 3 \: × \: 2 \: =$ ${ \bf {\rm \red {6 \: cm}}}$

Now,

We know,

${ \bf \boxed {\rm \red {Volume \: of \: the \: cuboid = \: l \: × \: b \: × \: h}}}$

$\therefore$$\bf Volume \: of \: the \: cuboid \: = \: 12 \: × \: 10 \: × \: 6 \: = \: 720 \: cm³$

Dimensions of the cuboid are ${ \bf {\rm \pink {12 \: cm \: ,}}}$ ${ \bf {\rm \red {10 \: cm \: ,}}}\: \&$ ${ \bf {\rm \purple {6 \: cm}}}$ [Ans]

Volume of the cuboid is ${ \bf {\rm \green {720 \: cm³}}}$ [Ans]

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