Question

Aditya has built a cubical water tank with a lid for his house with each outer edge equal to \[1.5\] m. He gets the outer surface of the tank including the base, covered with square tiles of side \[25\] cm. Find how much he would spend on tiles if the cost of tile is Rs \[480\] per dozen?

Answer 1

Hint: In the given question we have to find the total cost of tiles which will be spent by Aditya to make his cubical water tank so in order to find the cost first find the total area covered by tiles in that cubical water tank which you can find by converting \[1.5\] m to cm and then take the square of it because the area is always in square and then multiply it with 5 because there are total 5 sides to be covered. Then find the area of a single tile and then divide this area by the pool area then multiply with \[480\] you will get the desired result.

Complete step-by-step answer:
In the given question we have to find the total cost of tiles which will be spent by Aditya to make his cubical water tank for that we have given:
The outer edge of the tank \[ = 1.5m = 1.5 \times 100cm = 150cm\] (Because \[1m = 100cm\] )
Now Area of square \[ = Sid{e^2}\]
Now we have five sides of tank to be filled with tiles because the top face will be a lid so we get:
Surface area of tank \[ = 5 \times Sid{e^2}\]
 \[ \Rightarrow \] Surface area of tank \[ = 5 \times {150^2}\] (since the side of tank is \[150cm\] )
Now area of each tile \[ = til{e^2} = {25^2}\] (since side of tile is \[25cm\] )
Therefore the number of tiles required to form the water tank will be surface area of tank divided by surface area of tile i.e.
Number of tiles \[ = \dfrac{{5 \times 150 \times 150}}{{25 \times 25}} = 180\]
So total of \[180\] tiles are required to make the water tank
Now we have given \[12\] tiles cost RS. \[480\] because \[1\] dozen \[ = 12\]
Therefore, \[1\] tile will cost \[\dfrac{{480}}{{12}} = 40\]
There we need \[180\] tiles so total cost of tiles will be:
 \[180 \times 40 = 7200\]
Therefore Aditya needed Rs. \[7200\] to make his water tank.

Note: Here you should remember that first you have to convert all the terms in a single unit either meter or centimeter and then for the total area you have to do the square of the sides. Also you should notice that in the above question the price of tile is given dozen wise so first find the cost of a single tile and then calculate the total price.