Question

Hameed has built a cubical water tank with a lid for the house, with each outer edge 1.5m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25cm. find how much he would spend on tiles if the cost of tiles is Rs.360 per dozen.

Answer 1

Hint: The question is related to cube use the total surface area formula of the cube. Convert the length of the tank to the same measure unit, its meter, or centimeter. The rate of per dozen is given in the question simply multiply the area by the rate of per tile to get the total cost of tiles.

Complete step by step answer:
Given in the question that the length of the outer edge is 1.5m
First, convert the meter into centimeter
$ = 1.5m \times 100$
$ = 150cm$
So, now we have the length of the outer edge is 150 cm
The surface area of the water tank
$ = 5 \times sid{e^2}$
We have to take only 5 sides of the cube because the question mentioned that he get the surface of the tank excluding the base
Now put the value of side in the formula
$ = 5 \times {(150)^2}$
$ = 112500c{m^2}$
We have the surface area of the tank
Now find the area of a single tile
Side of the tile = 25cm
And tile is square in the shape
Area of the tile = $sid{e^2}$
Put the values of side in the formula
$ = {(25)^2}$
$ = 625c{m^2}$
Now we have to find the number of tiles required
$ = \dfrac{{{\text{surface area of tank}}}}{{{\text{area of tile}}}}$
$ = \dfrac{{112500}}{{625}}$
Divide the numerator by denominator
$ = 180$
The rate of per dozen tile is given which is Rs.360
First, we have to find the rate of a single tile
$ = \dfrac{{360}}{{12}}$
$ = 30$
Now multiply the number of tiles required by the rate of per dozen
$ = 180 \times 360$
$ = 5400$

Therefore, the total cost is Rs.5400

Note:
Students mostly do the mistake while multiplying the rate by the number of tiles they directly multiply the rate of per dozen with the area which is wrong first you have to find the rate of a single tile and then multiply the rate of a single tile with a number of tiles.