Question

dimensions of a room are 10×6×4m. the cost of white washing at re.1 per square m will be?

Answer 1

There are 3 cases for your question:

CASE 1 : If 4 walls + Floor + Roof are white-washed

CASE 2 : If 4 walls + Roof are white-washed

CASE 3 : If all 4 walls are white-washed

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We know that,

l = length of room = 10m

b= breadth of room = 6m

h = height of room = 4m

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CASE 1 : IF ( 4 WALLS + ROOF + FLOOR = 6 WALLS) ARE WHITE WASHED

Using the Formula,

2(lb + lh + bh)

Substituting the Values, We get,

$\mathsf{=> 2(10 \times 6) + (10 \times 4) + (6 \times 4)}\\\\\mathsf{=> 2(60 + 40 + 24)}\\\\\mathsf{=> 2 \times 124}\\\\\mathsf{=> 248 m^2}\\\\\textsf{Cost of White-Washing} \mathsf{\: = Re.1 / m^2}\\\\=> \textsf{Cost of White Washing 4 Walls \: =} \mathsf{\: 248 \times 1}\\\\ =>\boxed{\mathsf{ 248 \: Rupees}}$

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CASE 2 : IF (4 WALLS + ROOF = 5 WALLS) ARE WHITE WASHED

Using the Formula,

2(l + b)h + lb

Substituting the Values, We Get,

$\mathsf{=> 2(10 + 6) \times 4 + (10 \times 6)}\\\\\mathsf{=> 2(16)4 + 60}\\\\\mathsf{=> 128 + 60}\\\\\mathsf{=> 188 \: m^2}\\\\\textsf{Cost of White-Washing} \mathsf{\: = Re.1 / m^2}\\ \\\textsf{Cost of White-Washing 6 walls \: =} \mathsf{\: 188 \times 1}\\\\=> \boxed{\mathsf{Re. 188}}$

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CASE 3 : IF 4 WALLS ARE WHITE-WASHED

Using the Formula,

2(l + b)h

Substituting the Values, We get,

$\mathsf{=> 2(10 + 6) \times 4}\\\\\\\mathsf{=> 2(16) \times 4}\\\\\\\mathsf{=> 128 \: m^2}\\\\\\\textsf{Cost of White-Washing \: =} \mathsf{ \:\: Re.1 / m^2}\\\\\textsf{Cost of White-Washing 4 Walls \: =} \mathsf{128 \times 1}\\\\ => \boxed{\mathsf{Re. \: 128}}$

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