Question

The dimension of Mr. Narula’s bedroom is $8{\text{m}}\; \times 7{\text{m}} \times 5{\text{m}}.$ It has two windows, each measuring $2{\text{m}} \times 1{\text{m}}$ and one door measuring is $3{\text{m}} \times 1{\text{m}}{\text{.}}$Find the cost of white washing the room at Rs. 50 per square metre.

Answer 1

Hint: The white washing needed to be done on all the 6 sides of the room which is Cuboidal in shape. The area acquired by 2 windows and a door needed to be subtracting from the total area. As white washing can’t apply over the door.

Complete step-by-step answer:
 To get the cost of white washing, we need to calculate the total area of the Cuboidal which is given by $2\left( {{\text{lb}} + {\text{bh}} + {\text{hl}}} \right)$and here the dimensions given are $8 \times 7 \times 5{\text{m}}{\text{.}}$
So the total area of the Cuboidal is
\[\
  {\text{T}} \cdot {\text{A}}{\text{.}}\, = \,2\left( {8 \times 7 + 7 \times 5 + 5 \times 8} \right) \\
   = 2\left( {56 + 35 + 40} \right) \\
   = 2\left( {96 + 35} \right) \\
   = 2 \times 131 = 262{{\text{m}}^2}. \\
\]
The area acquired by windows and doors needed to be subtracted. So area is covered by window is
\[
  {\text{length}}\, \times \,{\text{width}}\,\, = \,2 \times 1 = 2{{\text{m}}^2} \\
  {\text{and}}\,{\text{by}}\,{\text{door}}\,\,{\text{is}}\,\,\,\,\,3 \times 1 = 3{{\text{m}}^2} \\
\]
So we, need to be subtract the area of the 2 windows and 1 door to obtain total area to white wash which is $262 - 2(2) - 3 = 255{{\text{m}}^{\text{2}}}$.
Hence, the total area to white wash is \[255\,{{\text{m}}^{\text{2}}}.\]Cost for white wash is Rs. 50 for $1\,{{\text{m}}^2}$ then for $255\,{{\text{m}}^{\text{2}}},$
Cost $ = 255 \times \,50 = \,{\text{Rs}}\,{\text{12750}}$.

Total cost will be Rs. 12,750.

Note: Major point over to mislead is covering all the walls for white wash even windows and door parts, but the windows and door acquiring the space is open and cannot be white wash. So, the total cost for white wash will be only for the front part which can be seen from the centre of the bedroom.