Question

The length, breadth and hieght of a room is 12m, 10m and 8m respectively . find the cost of a white washing its wall at the rate of Rs. 75 per m2 and cementing the floor at the rate of Rs. 100per m2.

Answer 1

Given :-  

》Dimensions of a room –  

• 12 m  is length  
• 10 m is breadth  
• 8 m is height  

》Cost of whitewashing is Rs. 75 per m²

》Cost of cementing floor is Rs. 100 per m²

To Find :-  

• The cost of doing the above mentioned activities in that room  

Solution :-  

~Here, firstly we will find the area to be white-washed which will be the four walls and the ceiling of the room . For the area of four walls , we can apply the formula of Curved Surface area and The area of ceiling can be found separately by the formula of area of a rectangle. By this area we need to multiply the cost per m. For cementing the floor of the room , only the area of rectangular floor will be needed.  

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Finding the area to be white-washed :-  

[ Area of four walls ]

★ CSA of cuboid = 2h( l + b )

$\sf \implies 2 \times 8( 12 + 10 )$

$\sf \implies 16(22)$

$\sf \implies 352\;m^{2}$

[ Area of ceiling ]  

★ Area of rectangle = length × breadth  

$\sf \implies 12\;m \times 10\;m$  

$\sf \implies 120\;m^{2}$  

[Total  Area :- ]  

352 m² + 120  m²

= 472 m²  

Finding the cost of white-washing :-

Cost of 1 m² = Rs. 75  

Cost of 472 m² = 472 × 75  

= Rs. 35,400

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Finding the area to be cemented :-

★ Area of rectangle = length × breadth  

$\sf \implies 12\;m \times 10\;m$

$\sf \implies 120\;m^{2}$

Finding the cost to cement :-  

Cost of 1 m² = Rs. 100  

Cost of 120 m² = 120 × 100  

= Rs. 12,000  

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Therefore,  

• Cost of whitewashing this room is Rs. 35400 and cost of cementing the floor is Rs. 12000  

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Answer 2

Concept Used -

Here the concept of surface area of cuboids in used. In order to find the cost of white washing the walls first we need to find the area which has to be white washed.

4 walls + ceiling = area that has to be white washed.

Similarly the cost of cementing can be found if we calculate the area of the floor.

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Formula Used-

$\diamond \bold{ \orange{Surface \: area \: of \: cuboid = 2h(l+b)}}\\ \\ \diamond\bold{ \pink{area \: of \: Rectangle= l×b}}$

where

• h denotes height
• b denotes Breath
• l denotes length

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Solution

We are aware of the fact that room is in cuboidal shape, so directly apply the formula of C.S.A

${ \underline{ \boxed{ \sf{ \color{pink}C.S.A = 2h(l+b)}}}}$

$\sf{ \implies C.S.A= 2 × 8( 12+10)} \\ \\ \sf{ \implies C.S.A =16 × 22} \\\\ \sf{ \implies C.S.A = 352 m²}$

Now

${ \underline{ \boxed{ \sf{ \color{grey}area \: of \: ceiling = l× b }}}}\\ \\ \sf {\implies area \: of \: ceiling= 12×10} \\ \\\sf{ \implies area \: of \: ceiling= 120 m²}$

$\sf{ \implies \: Total \: Area \: of \: white \: washing= 352 + 120 } \\ \\\sf{ \implies \: Total \: Area \: of \: white \: washing= 472 \: m²}$

$\sf{ \implies Rate \: of \: whitewashing = Rs \: 75 \: per \: m²} \\ \\ \sf{ \implies Cost \: of \: whitewashing \: 472 \: m²=472× 75}\\ \\ \sf{\implies Cost \: of \: whitewashing \: 472\:m²= Rs. \:35,400}$

~area of the floor will be same as that ceiling.

So,area of floor = 120 m²

$\sf{ \implies Rate \: of \: cementing= 100m²} \\ \\ \sf{ \implies cost of cementing 120 m²= 100 × 120} \\ \\ \sf{ \implies cost \: of \: cementing \: 120 \: m² = Rs. 12000 }$

Therefore the cost of whitewashing is Rs. 35400 and cementing the floor is Rs. 120000.

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