Question

The length, breadth and height of a room are 6 m, 5 m and 3.5 m respectively. The cost of white washing the walls of the room and the ceiling at the rate of Rs 8 per sq. m. is Rs

Answer 1

Given:-

• Length of the room = 6 m
• Breadth of the room = 5m
• Height of the room = 3.5 m

To find:-

The cost of white washing the walls and ceiling of the room at the rate of Rs. 8 per sq.m

Formula to be used:-

$\sf{Area\:of\:four\:walls = 2(Length + Breadth)\times Height\:\:sq.units}$

$\sf{Area\:of\:rectangle = Length\times Breadth\:\:sq.units}$

Solution:-

Length of the room = 6 m

Breadth of the room = 5 m

Height of the room = 3.5 m

$\sf{Area\:of\:four\:walls = 2(Length + Breadth)\times Height\:\:\:sq.units}$

= $\sf{Area\:of\:four\:walls = 2(6 + 5)\times 3.5\:\:m^2}$

= $\sf{Area\:of\:four\:walls = 2\times11\times3.5\:\:m^2}$

= $\sf{Area\:of\:four\:walls = 77\:m^2}$

Now,

$\sf{Area\:of\:the\:ceiling = Length\times Breadth\:\:\:sq.units}$

= $\sf{Area\:of\:the\:ceiling = 6\times5\:m^2}$

= $\sf{Area\:of\:the\:ceiling = 30\:m^2}$

$\sf{Total\:area\:of\:four\:walls\:and\:the\:ceiling = (77 + 30)\:m^2 = 107\:m^2}$

Now,

$\sf{Cost\: of\: white-washing\: 1m^2 = Rs.8}$

$\sf{Cost\:of\:white-washing\:107m^2 = Rs.(107\times8) = Rs.856}$

General Information:-

Area of four walls is also known as Lateral surface area of the room.

Some formulas:-

• $\sf{Area\:of\:Rectangle = (Length\times Breadth)\:sq.units}$

• $\sf{LSA\:of\:cuboid = 2(Length + Breadth)\times Height\:\:sq.units}$

• $\sf{Volume\:of\:cuboid = (Length\times Breadth\times \Height)\:cubic\:units}$

• $\sf{TSA\:of\:cuboid = 2(Length\times Breadth + Breadth\times Height + Height\times Length)\:sq.units}$

Note:-

TSA = Total Surface Area

LSA = Lateral Surface Area