Question

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

Answer 1

Step 1: Find the surface area of tank and one tile

We have,

Edge of the tank$=1.5\mathrm{m}=150\mathrm{cm}[\because 1\mathrm{m}=100\mathrm{cm}]$

Cost of $12$ tiles$=₹480$

Then,

Surface area of the tank$=5\times {\left(\mathrm{side}\right)}^2$

$$\begin{gathered} =5\times {\left(150\right)}^2 \\ =5\times 150\times 150{\mathrm{cm}}^2 \end{gathered}$$

Area of each tile $={\left(\mathrm{side}\right)}^2$

$=25\times 25{\mathrm{cm}}^2$

Step 2: Find the number of tiles

Therefore, number of tiles required$=\frac{\mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{tank}}{\mathrm{Area}\mathrm{of}1\mathrm{tile}}$

$$\begin{gathered} =\frac{5\times 150\times 150}{25\times 25} \\ =180\mathrm{tiles} \end{gathered}$$

Step 3: Find the total cost of tiles

We know that,

Cost of $12$ tiles$=₹480$

Cost of $1$ tile$=\frac{480}{12}=₹40$

Therefore, cost of $180$ tiles$=40\times 180=₹7200$

Hence, the required answer is $₹7200$ .