Question

marry wants to decorate her christmas tree . she wants to place the tree on a wooden box covered with coloured paper with picture of santa claus on it she must know the exact quantity of paper to buy for this purpose . If the box has length , breadth and height as 80cm , 40cm and 20cm respectively how many squares sheets of paper of side 40cm would she require

Answer 1

Answer:

Step-by-step explanation:

\begin{gathered}\frak Given = \begin{cases} &\sf{Length\ of\ the\ box\ =\ 80cm.} \\ &\sf{Breadth\ of\ the\ box\ =\ 40cm.} \\ &\sf{Height\ of\ the\ box\ =\ 20cm.} \end{cases}\end{gathered}

Given=

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Length of the box = 80cm.

Breadth of the box = 40cm.

Height of the box = 20cm.

To find:- We have to find the number of square sheets of paper required of side 40cm ?

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\frak{\underline{\underline{\dag As\ we\ know\ that:-}}}

†As we know that:−

\sf\pink{\underline{The\ surface\ area\ of\ the\ box\ =\ 2(lb\ +\ bh\ +\ hl).}}

The surface area of the box = 2(lb + bh + hl).

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\frak{\underline{\underline{\dag By\ substituting\ the\ values,\ we\ get:-}}}

†By substituting the values, we get:−

\begin{gathered} \sf : \implies {2\ [(80\ ×\ 40)\ +\ (40\ ×\ 20)\ +\ (20\ ×\ 80)]\ cm²} \\ \\ \sf : \implies {2\ [3200\ +\ 800\ +\ 1600]\ cm²} \\ \\ \sf : \implies {2\ ×\ 5600\ cm²} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf 11200cm².}}}}\bigstar \end{gathered}

:⟹2 [(80 × 40) + (40 × 20) + (20 × 80)] cm²

:⟹2 [3200 + 800 + 1600] cm²

:⟹2 × 5600 cm²

:⟹

11200cm².

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\frak{\underline{\underline{\dag The\ area\ of\ each\ sheet\ of\ the\ paper:-}}}

†The area of each sheet of the paper:−

\begin{gathered} \sf : \implies {40\ ×\ 40\ cm²} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf 1600cm².}}}}\bigstar \end{gathered}

:⟹40 × 40 cm²

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1600cm².

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\sf \therefore {\underline{Number\ of\ sheets\ required:-}}∴

Number of sheets required:−

\begin{gathered} \sf : \implies {\dfrac{surface\ area\ of\ box}{area\ of\ one\ sheet\ of\ paper}} \\ \\ \sf : \implies {\dfrac{11200}{1600}} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf 7\ sheets.}}}}\bigstar \end{gathered}

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area of one sheet of paper

surface area of box

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1600

11200

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7 sheets.

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Hence:-

\sf \therefore {\underline{So,\ she\ would\ require\ 7\ sheets.}}∴

So, she would require 7 sheets.

Answer 2

$\sf\underbrace{Understanding~the~question:) }$

• Since Mary wants to paste the paper on the outer surface of the box ; the quantity of paper required would be equal to the surface area of the box which is of the shape of a cuboid. The dimensions of the box are:

$\huge\bold{Given :}$

$\bf\blue{Length =}$ 80cm

$\bf\blue{Breadth =}$ 40cm

$\bf\blue{Height =}$ 20cm

$\bf\pink{let's~ do~ it!!}$

The surface are of the box = 2(lb+bh+hl)

${: \longrightarrow}$2[(80×40) + (40×20) + (20×80)] $cm^{2}$

${: \longrightarrow}$ 2[3200 + 800 + 1600] $cm^{2}$

${: \longrightarrow}$ 2 × 5600 $cm^{2}$ = 11200 $cm^{2}$

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The area of each sheet of the paper =

${: \longrightarrow}$40×40 $cm^{2}$

${: \longrightarrow}$1600cm $cm^{2}$

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Therefore number of sheets required, =

$\implies{\sf{\large { \:\:\: \dfrac{surface~ area~ of ~box }{area~of~ one ~sheet~ of ~paper}\: }}}$

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$\implies{\sf{\large { \:\:\: \dfrac{11200}{1600}\: }}}$

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$\implies{\sf{\large { \:\:\: \cancel \dfrac{11200}{1600}\: }}}$

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${↪}$$\sf\underline\red{7}$

$\bigstar{\bold{so, she~ would~ require~ 7 ~sheets. }}$