Question

. A rectangular cardboard sheet has length 32 cm and breadth 26 cm. The four squares each of side
3 cm are cut from the corners of the sheet and the sides are folded to make a rectangular container
Find the capacity of the container.
​

Answer 1

Given :

• Length = 32 cm
• Breadth = 26 cm
• Four squares of each side = 3 cm

To Find :

• Capacity of the container (Volume).

Calculation :

Firstly, we'll be calculating the inner length & breadth of the container.

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${ \dag \: \: { \underline \frak{Calculating \: for \: length :}}}$

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$: \bf \Longrightarrow \bf (32 - 3 - 3) \: cm \\ \\ \\ : \bf \Longrightarrow \bf \: 29 - 3 \: cm \\ \\ \\ : \bf \Longrightarrow { \boxed{\bf{26 \: cm}}} \: \bigstar$

Therefore, the inner length of the container is 26 cm.

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${ \dag \: \: { \underline \frak{Calculating \: for \: breadth :}}}$

$: \bf \Longrightarrow \bf (26 - 3 - 3) \: cm \\ \\ \\ : \bf \Longrightarrow \bf \: 23 - 3 \: cm \\ \\ \\ : \bf \Longrightarrow { \boxed{\bf{20 \: cm}}} \: \bigstar$

Therefore, the inner breadth of the container is 20 cm.

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• Also, height of the container is 3 cm.

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$\dag \: { \underline { \bf{According \: to \: the \: Question, }}}$ ⠀⠀⠀⠀⠀⠀⠀

Let's calculate the volume of the container,

Formula to be used :

$\star \boxed{ \sf{ \purple{Volume = length \times breadth \times height }}}$

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Where,

• Height ($\pmb{h}$) = 3 cm
• Length ($\pmb{l}$) = 26 cm
• Length ($\pmb{b}$) = 20 cm

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$\dag$ Putting the values,

$: \bf \Longrightarrow \bf \: Volume = l \times \ b \times h \\ \\ \\ : \bf \Longrightarrow \bf \: Volume \: = 26 \times 20 \times 3 \: cm \\ \\ \\ : \bf \Longrightarrow { \boxed{\bf Volume \: = \: 1560 \: cm^3}} \: { \pink{ \bigstar}}$

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$\therefore$ Hence, the volume of the container is 1560 cm³.

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${ \green{ \bigstar}} \: \: { \underline{ \bf{Diagram :}}}$

$\setlength{\unitlength}{0.9cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 32 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 26 cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$