Question

Unni has a cubicle room of his own whose total surface area is 216m. Find the cost of distempering the four walls of the room at the rate of Rs.40 per m².
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Answer 1

Refer to the above attachment

Answer 2

$\large\underline\mathrm\red{Given:-}$

• $\small\mathrm{Total \: surface \: area \: of \: the \: cubical \: room \: = \: 216 \: {m}^{2}}$

$\large\underline\mathrm\red{To \: find}$

• $\small\mathrm{What \: is \: the \: cost \: of \: distempering \: the \: four \: walls \: of \: the \: room \: at \: the \: rate \: of \: 40 \: per \: {m}^{2}?}$

$\large\underline\mathrm\red{Solution}$

• $\small\mathrm{Let \: the \: side \: of \: the \: cubical \: room \: be \: x \: m}$

• $\small\mathrm{We \: know \: that \: the \: formula \: for \: finding \: the \: Total \: surface \: area \: of \: the \: cubical \: room \: is:-}$

$\large\underline\mathrm\red{{\star \: AREA = 6 {(side)}^{2} \: \star }}$

$\large\underline\mathrm\red{According \: to \: questions:-}$

$\small\mathrm{On \: putting \: the \: given \: values \: in \: the \: formula, \: we \: get}$

$\small\mathrm{⇢{216} = {6(x)}^{2}}$

$\small\mathrm{⇢{216} = {6x}^{2}}$

$\small\mathrm{⇢{216}/{6} = {x}^{2}}$

$\small\mathrm{⇢{36} = {x}^{2}}$

$\small\mathrm{⇢ root{36} = {x}}$

$\small\mathrm{⇢{6} m = {x}}$

$\large\underline\mathrm\red{The \: side \: of \: the \: cubical \: room \: is \: 6m}$

$\small\mathrm{Now, \: we \: have \: to \: find \: the \: area \: of \: four \: falls.}$

$\small\mathrm{We \: know \: that \: the \: formula \: for \: finding \: the \: Curved \: surface \: area \: of \: the \: cubical \: room \: is:-}$

$\large\underline\mathrm\red{\star \: AREA = 4 {(side)}^{2} \: \star}$

$\large\underline\mathrm\red{According \: to \: questions:-}$

$\small\mathrm{On \: putting \: the \: given \: values \: in \: the \: formula, \: we \: get}$

$\small\mathrm{⇢{Area = {4} × {(6)}^{2}}}$

$\small\mathrm{⇢{Area} = {4} × {36}}$

$\small\mathrm{{\star \: Area = 144 \: {m}^{2} \: \star }}$

⇢ 1 m² = Rs. 40

⇢ 144 m² =  40 ×  144 =  Rs.5760

❝Hence, the cost of distempering the 4 walls of the room is  Rs.5760❞

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