Question

Seem wants to decorate a model .She wants to place the model on a wooden box covered with coloured paper with picture of some hero on it. She must know the exact quantity of paper to buy for this purpose . If tje box has length, breadth and height as 60 cm , 30 cm and 15 cm respectively , then how many square sheets of paper of side 30 cm would she require ?


please answer
with explanation​

Answer 1

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Concept}}}$

Here the Concept of Total Surface Area of Cuboid and Area of square has been used. We know that the area of coloured paper needed to cover the wooden box will be equal to the Total Surface Area of wooden box which is cuboidal in shape. Also this area of paper used will also be equal to the sum of areas of sheet of square papers required to cover box.

Let's do it !!

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★ Equations Used :-

$\\\;\boxed{\sf{TSA\;of\;Cuboid\;=\;\bf{\pink{2(lb\;+\;bh\;+\;lh)}}}}$

$\\\;\boxed{\sf{Area\;of\;Square\;=\;\bf{\pink{(Side)^{2}}}}}$

$\\\;\boxed{\sf{No.\;of\;sheets\;required\;=\;\bf{\pink{\dfrac{TSA\;of\;Box}{Area\;of\;each\;sheet}}}}}$

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★ Solution :-

Given,

» Length of box = L = 60 cm

» Breadth of box = B = 30 cm

» Height of box = H = 15 cm

» Side of each square sheet = 30 cm

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~ For the TSA of Wooden Box ::

We know that,

$\\\;\sf{:\rightarrow\;\;TSA\;of\;Cuboid\;=\;\bf{2(lb\;+\;bh\;+\;lh)}}$

Now by applying values, we get

$\\\;\sf{:\Longrightarrow\;\;TSA\;of\;Cuboid\;=\;\bf{2[(60)(30)\;+\;(30)(15)\;+\;(60)(15)]}}$

$\\\;\sf{:\Longrightarrow\;\;TSA\;of\;Cuboid\;=\;\bf{2[1800\;+\;450\;+\;900]}}$

$\\\;\sf{:\Longrightarrow\;\;TSA\;of\;Cuboid\;=\;\bf{2[3150]}}$

$\\\;\bf{:\Longrightarrow\;\;TSA\;of\;Cuboidal\;Box\;=\;\bf{\orange{6300\;\;cm^{3}}}}$

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~ For the Area of Each Square Sheet ::

We know that,

$\\\;\sf{:\rightarrow\;\;Area\;of\;Square\;=\;\bf{(Side)^{2}}}$

By applying values, we get

$\\\;\bf{:\Longrightarrow\;\;Area\;of\;Square\;=\;\bf{(30)^{2}}}$

$\\\;\bf{:\Longrightarrow\;\;Area\;of\;Square\;=\;\bf{\orange{900\;\;cm^{2}}}}$

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~ For the Number of Square sheets needed ::

We know that,

$\\\;\sf{:\rightarrow\;\;No.\;of\;sheets\;required\;=\;\bf{\dfrac{TSA\;of\;Box}{Area\;of\;each\;sheet}}}$

Now by applying values, we get

$\\\;\sf{:\Longrightarrow\;\;No.\;of\;sheets\;required\;=\;\bf{\dfrac{6300}{900}}}$

$\\\;\bf{:\Longrightarrow\;\;No.\;of\;sheets\;required\;=\;\bf{\green{7}}}$

$\\\;\underline{\boxed{\tt{Hence,\:\;no.\;\:sheets\;\:required\;=\;\bf{\purple{7}}}}}$

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★ More Formulas to know :-

$\\\;\sf{\leadsto\;\;CSA\;of\;Cuboid\;=\;2(L\;+\;B)\:\times\:H}$

$\\\;\sf{\leadsto\;\;Volume\;of\;Cuboid\;=\;Length\:\times\:Breadth\:\times\:Height}$

$\\\;\sf{\leadsto\;\;Perimeter\;of\;Square\;=\;4\;\times\;Side}$

$\\\;\sf{\leadsto\;\;Diagonal\;of\;Square\;=\;Side\:\times\:\sqrt{2}}$

Answer 2

the angry master bro qpwoeir