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A marble tile measures$12cm \times 12cm$. How many tiles will be required to cover a wall of size 4m by 3m? Also, find the total cost of the tiles at Rs. 22.50 per tile.

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Last updated date: 20th Jun 2024
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Answer
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Hint:
Marbles is a very familiar word for all of us. We used it in our home for floor making. Here marble size is given to be $12cm \times 12cm$, so area of one marble is $144c{m^2}$ and we have to cover the whole wall whose dimension is given to be $4m \times 3m$ and so area is . $12{m^2}$

Complete step by step solution:
Dimension of marbles =$12cm \times 12cm$
Dimension of wall = $4m \times 3m$
Cost of tiles is given to be Rs. 22.50
Let’s begin to solve our question. First we need to calculate how much tile we need to cover the wall. If we gradually stick the entire marble one by one we find that the total area of the wall is n times the area of one marble.
${\text{area of wall = n }} \times {\text{ area of marble}}$
Calculate the area of marble and the wall
Area of the marble can be calculated as $12cm \times 12cm = 12{m^2}$
Area of the wall can be calculated as $4m \times 3m = 12{m^2}$
Number of tiles required:
 Number of tiles required to cover the wall is
 $
 = \dfrac{{12 \times 10000}}{{144}} \\
 = 383.3 \\
 = 384 \\
$
We can’t buy $\dfrac{1}{3}$ titles from the market so we have to buy one more tile. That’s why we add 1 in 384.
Let’s move on to the second part of this question to calculate the expenditure for covering the wall with tiles.
Step 2 we can calculate total cost by using the formula
$
  {\text{Total cost = number of marbles }} \times {\text{ cost of each tile}} \\
  {\text{ = 834}} \times {\text{22}}{\text{.50}} \\
  {\text{ = 18765 Rs}}{\text{.}} \\
$

Note:
As we know, tile can’t be bought in fraction, so we have to buy complete one tile for $\dfrac{1}{3}$ of tile used. Sometimes students neglect the $\dfrac{1}{3}$ part of the tile which is totally wrong as per the concepts.