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The length of a room is three times its breadth and its volume is 240 m. The cost of plastering its four walls at Rs. 50 per square meter is Rs. 8000, find the height of the room. (Ans: 5 m)​

Sagot :

ⲊⲧɑⲅⲊⲏɑᴅⲟᏇ

Ⲁⲛ⳽ⲱⲉⲅ :

  • 5m

Ⲋⲟⳑⳙⲧⳕⲟⲛ :

We are given that:

  • The length of the room is three time it's breadth.
  • Volume of the room is 240m³
  • Cost of plastering 4 walls is Rs.8000
  • Cost of plastering 1 wall is Rs.50

Some assumptions:

  • Let the breadth be x
  • Then length will be 3x
  • Let the height be h

Using Formula:

  • Volume = l × b × h

➙ V = l × b × h

➙ V = x × 3x × h

➙ 240 = 3x² × h ‎ㅤ‎ㅤ⸻ ( 1 )

Now, the cost of plastering it's 4 walls is Rs 8000 at the rate of 50 /m². So, we can find the area of the walls of the room by dividing 8000 by 50 i.e:

➙ A = Total cost / cost per m²

➙ 8000 / 50

➙ 800 / 5

➙ 160m²

In a cuboid , there are a pair of two opposite and equal rectangular sides, and area of rectangle is given by :

  • l × b

So, area of 2 walls along length :

➙ 2 × length × height

➙ 2 × 3x × h

➙ 6xh

Area of 2 walls along breadth:

➙ 2 × breadth × height

➙ 2 × x × h

➙ 2xh

Sum of areas of these four walls will be equal to the area of the walls, that we have find earlier;

➙ ( 6xh ) + ( 2xh ) = 160

➙ 8xh = 160

➙ xh = 160 / 8

➙ xh = 20 ‎ㅤ‎ㅤ‎ㅤ⸻ ( 2 )

  • Using equation ( 1 )

➙ 240 = 3x²h

➙ x²h = 240 / 3

➙ x × xh = 80

➙ x × 20 = 80 ‎ㅤ‎[ from equation ( 2 ) ]

➙ x = 80 / 20

➙ x = 4

  • Using equation ( 2 )

➙ xh = 20

➙ 4 × h = 20

➙ h = 20 / 4

➙ h = 5

‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ~Hence, the height of the room is 5m.

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