Question

the length,breadth and height of a room are 10cm,8cm and 6cm.find the cost of white washing the walls of the room at the rate of rupees 8 per cm².​

Answer 1

Step-by-step explanation:

$\large \frak{Given} :$

• Length of the room = 10cm
• Breadth of the room = 8cm
• Height of the room = 6cm
• And the cost of white washing of walls = 8 per cm²

$\large \frak{To \: find : }$

• Find the Total cost of white washing of room?

$\large \green{ \frak{Solution : }}$

$\green{\begin{gathered}\frak{we\;have}\begin{cases}\sf{\:\; \: Length = \bf{10\;cm}}\\\sf{ \: \: \: Breadth = \bf{8 \;cm}}\\\sf{ \: \: \:height = \bf{6 cm }}\end{cases}\end{gathered}}$

We white wash the foot walls and the ceiling of the room

$\boxed{ \sf \: Area \: of \: the \: white \: wash = Area \: of \: cube - Area \: of \: base}$

• Area of cube = 2 ( LB + BH + LH)
• Area of base = L × B

$\: \qquad \longmapsto \sf \: 2(LB + BH + LH) - lb$

$\: \qquad \longmapsto \sf \: 2(LB) + 2(BH) + 2(LH) - LB$

$\: \qquad \longmapsto \sf \: \: LB + 2(BH) + 2( LB)$

$\: \qquad \longmapsto \sf \: [(10×8) + (2×8×6)+(2×10×6)]cm²$

$\: \qquad \longmapsto \sf \: [80 + 96 + 120]cm²$

$\: \qquad \longmapsto \frak{ \: 296cm²}$

Cost of white washing per cm² = Rs. 8

Cost of white washing 296cm² = Rs. ( 296 × 8) =Rs. 2368

Hence, the cost of white washing the walls is Rs. 2368

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Information

• L = length
• B = breath
• H = Height

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Answer 2

Given :-

Length = 10cm

Breadth = 8cm

height = 6cm

➪ Area of four walls of the room is : 2 × h × (l+b)

Solution :-

Area :

$\sf{⟹ 2 × h × (l+b)}$

$\sf{⟹ 2×6(10+8)}$

$\sf{⟹ 12 × 18}$

$\sf⟹ {216m}^{2}$

Area of the ceiling is:

$\sf{Area = L × B}$

$\sf{⟹ 10 × 8}$

$\sf⟹ {80m}^{2}$

Total area of the four walls and the ceiling of the room is :

$\sf⟹ 216 + 80 ⟹ {296}^{2}$

$\sf{It \: is \: given \: that \: cost \: of \: white \: washing \: is \: {8m}^{2} }$

Therefore,

Total cost of white washing is:

$\sf{⟹296×8}$

$\sf{⟹ 2368}$

★Hence, the cost of white washing the walls is Rs. 2368.