2450 piece of blocks each of side 20 cm are required to construct a wall of 15m long and 40 cm width. If the wall has a door of 2.5m×1m and a window of 2m×3m,what is the height of the wall ?
Answers
Given,
The number of blocks = 2450
The length of one side of the block = 20 cm
The length of wall = 15 metres = 1500 cm
The width of wall = 40 cm
The dimensions of door = 2.5 m × 1 m = 250 cm × 100 cm
The dimensions of window = 2 m × 3 m = 200 cm × 300 cm
To find,
The height of the wall.
Solution,
Volume of one block = (20 cm)³ = 8000 cm³
Volume of the actual wall = 2450 × 8000 = 19600000 cm³ ...(1)
Volume of door = 250×100×40 = 1000000 cm³
Volume of window = 200 × 300 × 40 = 2400000 cm³
Total volume of door and window = (1000000 + 2400000) = 3400000 cm³
Let,the height of the wall = h cm
The total volume of the wall = 1500×h×40 = 60000h cm³
The actual volume of the wall = (60000h - 3400000) cm³....(2)
Now, if we compare 1 and 2, we will get the following mathematical equation,
60000h - 3400000 = 19600000
60000h = 19600000-3400000
60000h = 16200000
h = 270
Height = 270 cm = 2.7 metres
Hence,the height of the wall is 2.7 metres.