The length of a wall is 10 m, width is 0.5 m and height is 2 m. Bricks of size 25 cm 12 cm 8 cm are used to build the wall. Also, 110 part of the wall is occupied by the clay joints. a) How many…

Solution

a) Number of bricks required

Step 1: Calculate the volume of the wall The wall is a cuboid with dimensions:

• Length ($L$) = 10 m = 1000 cm
• Width ($W$) = 0.5 m = 50 cm
• Height ($H$) = 2 m = 200 cm

Volume of the wall ($V_{\text{wall}}$) is given by: $$V_{\text{wall}}=L\times W\times H=1000\times 50\times 200=10,000,000{\text{ cm}}^3$$

Step 2: Calculate the volume occupied by clay joints $\frac{1}{10}$ of the wall is occupied by clay joints, so the volume of bricks ($V_{\text{bricks}}$) is: $$V_{\text{bricks}}=V_{\text{wall}}-\left(\frac{1}{10}\times V_{\text{wall}}\right)=\frac{9}{10}\times V_{\text{wall}}=0.9\times 10,000,000=9,000,000{\text{ cm}}^3$$

Step 3: Calculate the volume of one brick Each brick has dimensions:

• Length = 25 cm
• Width = 12 cm
• Height = 8 cm

Volume of one brick ($V_{\text{brick}}$) is: $$V_{\text{brick}}=25\times 12\times 8=2,400{\text{ cm}}^3$$

Step 4: Calculate the number of bricks required Number of bricks ($N$) is: $$N=\frac{V_{\text{bricks}}}{V_{\text{brick}}}=\frac{9,000,000}{2,400}=3,750$$

Final Answer: 3,750 bricks are required to construct the wall.

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b) Estimate the cost of bricks

Step 1: Calculate the cost per brick The cost of 1000 bricks is Rs. 14,500. Cost per brick is: $$\text{Cost per brick}=\frac{14,500}{1,000}=14.5\text{ Rs.}$$

Step 2: Calculate the total cost Total cost for 3,750 bricks is: $$\text{Total cost}=3,750\times 14.5=54,375\text{ Rs.}$$

Final Answer: The estimated cost of bricks is Rs. 54,375.

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