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Maths-

General

Easy

Question

The dimensions of a cuboid are in the ratio of 4:3:2 and its total surface area is 1300 cm². Find its length, breadth, and height respectively?

10 cm , 15 cm, 20 cm
15 cm , 10 cm ,20 cm
15 cm , 20 cm , 10 cm
20 cm,15cm , 10 cm

hint Hint:

We have given three different dimensions of rectangular box (cuboid) ,
Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
where
l → length of the cuboid
b → breadth of the cuboid
h → height of the cuboid

The correct answer is: 20 cm,15cm , 10 cm

Given: Ratio of dimensions of a cuboid is 4:3:2 & The Total surface area of cuboid is 1300 cm².
We have to find Length, breadth & height of cuboid.

Let length, breadth and height of cuboid be 4x, 3x and 2x respectively.⠀⠀

Now, As we know that, total surface area of cuboid is given by,

Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
where, l, b & h are length, breadth and height of cuboid respectively.

We have , length = 4x

Breadth, b = 3x
Height, h = 2x
TSA = 1300 cm²

Putting the values in the formula

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 2 left square bracket left parenthesis 4 x right parenthesis left parenthesis 3 x right parenthesis plus left parenthesis 3 x right parenthesis left parenthesis 2 x right parenthesis plus left parenthesis 2 x right parenthesis left parenthesis 4 x right parenthesis right square bracket equals 1300 end cell row cell 2 open square brackets 12 x squared plus 6 x squared plus 8 x squared close square brackets equals 1300 end cell row cell 2 open parentheses 26 x squared close parentheses equals 1300 end cell end table$

Dividing both sides of equation by 2

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 26 x squared equals 1300 over 2 end cell row cell 26 x squared equals 650 end cell end table$

Dividing both sides of equation by 26

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x squared equals 650 over 26 end cell row cell x squared equals 25 end cell row cell x equals square root of 25 end cell row cell x equals 5 end cell end table$
Therefore,
The dimensions of cuboid are,
Length = 4x = 4(5)= 20
Breadth= 3x = 3(5) =15
Height = 2x=2(5)= 10
$therefore$ Thus, The length, breadth & height of cuboid are 20 cm, 15 cm & 10 cm respectively.
Therefore the correct option is d) 20 cm,15cm , 10 cm

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