Math, asked by khyatidagar6, 4 months ago

the ratio of length breadth and height of cubiod is 6:5:3 . Find the length of the cubiod of total surface area is 1332sq.cm.
Options
1) 12cm
2.15cm
3.18cm
4.20cm​

Answers

Answered by Anonymous
14

\large\sf\underline{Understanding\:the\:concept\::}

Here in the question we are given the ratio of length breadth and height of cuboid as 6 : 5 : 3 . We will first assume the length, breadth and height of cuboid using some similar term . Then in the question it's also given the total surface area ( TSA ) of cuboid as 1332 sq.cm . We also know the formula for total surface area of cuboid. So now we will equate the given value and the formula of total surface area. Doing so we will get the measure of length, breadth and height of the cuboid. Lets begin!

\large\sf\underline{Given\::}

  • Ratio of cuboid = 6 : 5 : 3 .

  • TSA of cuboid = 1332 sq. cm.

\large\sf\underline{To\:find\::}

  • Length of the cuboid.

\large\sf\underline{Assumption\::}

According to question , Ratio of cuboid is given as 6 : 5 : 3 .

Now let :

  • Length of the cuboid be 6x .

  • Breadth of the cuboid be 5x .

  • Height of the cuboid be 3x .

\large\sf\underline{Solution\::}

We know,

\large{\underline{\boxed{\mathrm\pink{TSA\:of\:cuboid\:=\:2(lb+bh+hl)}}}}

where,

  • l = length of the cuboid

  • b = breadth of the cuboid

  • h = height of the cuboid

Substituting the given and assumed value in the formula :

\sf\implies\:1332\:=\:2[(6x \times 5x) +(5x \times 3x) + (3x \times 6x) ]

\sf\implies\:1332\:=\:2[30x^{2} + 15x^{2} + 18x^{2}]

\sf\implies\:1332\:=\:2[63x^{2}]

\sf\implies\:1332\:=\:2 \times 63x^{2}

\sf\implies\:1332\:=\:126x^{2}

  • Transposing 126 to other side

\sf\implies\:\cancel{\frac{1332}{126}}\:=\:x^{2}

\sf\implies\:\cancel{\frac{666}{63}}=\frac{222}{21}\:=\:x^{2}

\sf\implies\:10.5\:=\:x^{2}

  • Transposing square to the other side

\sf\implies\:\sqrt{10.5}\:=\:x

\large{\mathfrak\red{\implies\:x=\:3.25\:cm}}

So now let's substitute the value of x in the assumed value of length , breadth and height :

  • Length = 6x = 6 × 3.25 = {\sf{{\green{19.5\:cm}}}}

  • Breadth = 5x = 5 × 3.25 = {\sf{{\green{16.25\:cm}}}}

  • Height = 3x = 3 × 3.25 = {\sf{{\green{9.75\:cm}}}}

\dag\:\underline{\sf So\:the\:required\:length\:of\:the\:cuboid\:is\:19.5\:cm}

◎ But there is no option as measure of length to be 19.5 cm .

We do know from the rounding off rule that : When the number to be dropped ( here 5 ) is greater or equal to 5 then we need to add 1 to the preceding number ( here 9 ) if the number is odd.

So we know 9 is odd so adding 1 to 19 we get 20 .

\small\fbox\blue{Length\:of\:cuboid\:=\:20\:cm}

!! Hope it helps !!

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