Question

the internal measure of cuboidal room are 12m× 8m×4m×.find the total cost of whitewashing all four walls of a room, if the cost of white washing is rs5per m^2 .what will be the cost of white washing if the ceiling of the room is also whitewashed.​

Answer 1

$\huge \underline \mathbb {SOLUTION:-}$

$\bold\red{Cost\:of\:white\:washing\:4\:walls} = \bold{Rs.800}$

$\bold\green{Total\: Cost} = \bold{Rs.1280}$

Step-by-step explanation:

$\bf\red{Given:-}\begin{cases}\sf\red{Length = 12\:m}\\\sf\green{Breadth=8\:m}\\\sf\orange{Height = 4\:m}\\\sf\green{Rate = Rs.5 \: per\:{m}^{2} }\end{cases}$

$\bf\red{To\:find:-}\begin{cases}\sf\green{Cost\:of\:white\:washing\:4\:walls=?}\\\sf\purple{Cost\:of\:whitewashing\:including\:ceiling=?}\end{cases}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

$\bigstar\sf\red{ We\:know\:that:-}$

${\boxed{\sf\green{Area\:of\:4\:walls = 2(l + b)\times h}}}$

$\Rightarrow\sf\green{Area\:of\:4\:walls = 2(12 + 8)\times 4 }$

$\Rightarrow\sf\red{Area\:of\:4\:walls = 2 \times 20 \times 4}$

$\Rightarrow\sf\purple{Area\:of\:4\:walls = 160\:{m}^{2} }$

$\bigstar\sf\green{Cost\:of\:whitewashing = Area \times Rate }$

$\Rightarrow\sf\red{Cost\:of\:whitewashing =Rs. (160 \times 5) }$

$\Rightarrow{\boxed{\sf\green{Cost\:of\:whitewashing = Rs.800}}}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

$\sf\red{We\:know\:that,}$

${\boxed{\bold\red{Area\:of\:ceiling = l \times b}}}$

$\Rightarrow\sf\green{Area\:of\:ceiling = 12 \times 8 }$

$\Rightarrow\sf\orange{Area\:of\:ceiling = 96\:{m}^{2}}$

$\bigstar\sf\green{Cost = Area \times Rate}$

$\Rightarrow\sf\red{Cost = Rs.(96\times 5) }$

$\Rightarrow\sf\orange{Cost = Rs.480 }$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

$\bigstar\sf\red{Total\:cost = Rs.(800 + 480)}$

$\Rightarrow{\boxed{\sf\purple{Total\:cost = Rs.1280}}}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$