Question

The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the
cost of white washing the walls of the room and the ceiling at the rate of
7.50 per m2.​

Answer 1

$\frak{Given}\begin{cases}\sf{\: Length \ of \ room \ is \ \bf{5\: m}}\\\sf{\: Breadth \ of \ room \ is \ \bf{4 \: m}}\\\sf{\: Height \ of \ room\ is \ \bf{3 \ m}}\end{cases}$

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$\star$ DIAGRAM:

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$\setlength{\unitlength}{0.68cm}\begin{picture}(12,4)\linethickness{0.3mm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\qbezier(6,6)(4,7.3)(4,7.3)\qbezier(6,9)(4,10.2)(4,10.3)\qbezier(11,9)(9.5,10)(9,10.3)\qbezier(11,6)(10,6.6)(9,7.3)\put(8,5.5){\sf{l=4}}\put(4,6){\sf{b= 4}}\put(11.5,7.5){\sf{h=3}}\end{picture}$⠀⠀

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$\star\:{\underline{\boxed{\sf{\pink{Area \ of \ ceiling = Length \times Breadth}}}}}$

$:\implies\sf 5 \times 4 \\\\\\:\implies\boxed{\frak{\purple{ 20\: sq \ m}}}$

$\star\:{\underline{\boxed{\sf{\pink{Area \ of \ four \ walls = 2h(Length+ Breadth)}}}}}$

$:\implies\sf 2 \times 3 (5 + 4) \\\\\\:\implies\sf 6 \times 9\\\\\\:\implies\boxed{\frak{\purple{54 \ sq \ m}}}$

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Therefore,

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$:\implies\sf 54 + 20 \\\\\\:\implies\sf 74$

Area of walls & ceiling of room is 74 m².

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☯ Given that, cost of white washing is 7.50 per m².

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$:\implies\sf Total \ cost \ of \ white \ washing = 74 \times 7.50 \\\\\\:\implies{\underline{\boxed{\frak{\pink{Rs. \ 555}}}}}$

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$\therefore\;{\underline{\sf{Hence,Cost \ of \ white \ washing \ is \ {\textsf{\textbf{Rs. 555}}}.}}}$

Answer 2

Given :-

• Length of room = 5 m
• Breadth of room = 4 m
• Height of room = 3 m
• Cost of white washing per m² = Rs. 7.5

To Find :-

• Cost of white washing wall and ceiling at rate of 7.5 m².

Formula used :-

• Area of four walls = 2h ( l + b )
• Area of ceiling = Length × Breadth

Solution :-

→ Area of four walls = 2h ( l + b )

= 2 × 3 ( 5 + 4 )

= 2 × 3 ( 9 )

= 2 × 27

= 54 m²

→ Area of four walls = 54 m²

→ Area of ceiling = Length × Breadth

= 5 × 4

= 20 m²

→ Area of ceiling = 20 m²

Total area of ceiling and four walls

= 54 + 20 = 74

→ Total area of ceiling and four walls = 74 m²

Given that, Cost of white washing per m² = Rs. 7.5

Total cost = Cost per m² × Area of ceiling and four walls

= 7.5 × 74

= 555

Total cost of white washing = Rs. 555