Question

6. The walls and ceiling of a hall 32 m long, 22 m wide and 12 m high are to be covered with a wall
paper. Find the length of paper required if the paper is 2 m wide.
7. The length and breadth of a rectangular field is 100 m and 70 m respectively. If three layers o
wires are used to fence it, how much wire is needed?​

Answer 1

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$\bf \red{Question}$

$\bf\scriptsize \: {The \: walls \: and \: ceiling \: of \: a \: hall \: 32 \: m \: long, } \\ \bf \scriptsize{22 \: m \: wide \: and \: 12 m \: high \: are \: to \: be \: covered \: with \: a \: wall} \\\bf\scriptsize{paper. \: Find \: the \: length \: of \: paper \: required \: if \: the \: paper is \: 2 m \: wide.}$

$\bf \red{Answer}$

$\bf \scriptsize{We \: know \: that \: Lateral \: surface \: area \: of \: cuboid \: is \: = 2 \times height( \: length \: + \: width \: )} \\ \bf \scriptsize{ \: = 2 \times h \: ( \: l + b)}$

$\bf \scriptsize{ = 2 \times h \: ( \: l \: + \: b) } \\ \bf \scriptsize{ = 2 \times 12 \: (32 + 22) \: } \\ \bf \scriptsize{ = 24 \: (54)} \\ \bf \scriptsize{ = 25 \times 54} \\ \bf \scriptsize{ = 1266}$

$\bf \scriptsize{Length \: of \: the \: paper \: required \: = \frac{lateral \: surface \: area \: of \: cuboid \: }{ \: wide \: paper} }$

$\bf \scriptsize{ = \frac{1296}{2} = 634.5 \: m}$

$\bf \scriptsize{Hence \: length \: of \: \: paper \: is \: 634.5 \: m \: required.}$

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$\bf \red{Question}$

$\bf \scriptsize{The \: length \: and \: breadth \: of \: a \: rectangular \: field \: is \: 100 \: m \: and \: 70 m \: respectively \: . If \: three \: layers \: of} \\\bf \: \scriptsize{wires \: are \: used \: to \: fence \: it, \: how \: much \: wire \: is \: needed? \: }$

$\bf \red{Answer}$

$\bf\scriptsize{ Wire \: required = perimeter \: of \: field \: \times \: no. \: of \: layers \: } \\ \bf\scriptsize{ = 2( \: l + b) \times 3} \\ \bf\scriptsize{ = 2(100 + 70) \times 3} \\ \bf \scriptsize{ = 340 \times 3} \\ \bf \scriptsize{ = 1020 \: m \: }$

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Answer 2

answer is in attachment