Question

The paint in a certain container is sufficient to paint an area equal to 9.375 ${{m}^{2}}$. How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?

Answer 1

Hint: We are given the area which the paint in the container can cover. Our objective is to paint as many bricks as we can with the same amount of paint. This problem has to be solved using a unitary method. To begin with, we will find the area on each brick which needs to be painted. That area will be the surface area of the brick. We can find the surface area of the cuboidal brick by the relation given as SA = 2(lb + bh + hl). Once we find the surface area of one brick, we can calculate how many of these bricks make 9.375 ${{m}^{2}}$. Thus, we can find the number of bricks which can be painted and whose cumulative surface area is equal to 9.375 ${{m}^{2}}$ by dividing the total area by surface area of individual bricks.

Complete step by step answer:
We are given that the paint in a certain container is sufficient to paint an area equal to 9.375 ${{m}^{2}}$. The dimensions of the brick are 22.5 cm × 10 cm × 7.5 cm.
Thus, the length l of the brick is 22.5 cm, breadth b of the brick is 10 cm and height h of the brick is 7.5 cm. The brick will look as follows:
 

We need to paint every face of the brick. Hence, the area to be painted in a single brick will be equal to its surface area. We can find the surface area of the cuboidal brick by the relation given by the formula SA = 2(lb + bh + hl).
$\Rightarrow $ SA = 2(22.5 $\times $ 10 + 10 $\times $ 7.5 + 22.5 $\times $7.5) $c{{m}^{2}}$
$\Rightarrow $ SA = 2(225 + 75 + 168.75) $c{{m}^{2}}$
$\Rightarrow $ SA = 2(468.75) $c{{m}^{2}}$
$\Rightarrow $ SA = 937.5 $c{{m}^{2}}$
Now, we need to find how many of these bricks with a surface area 937.5 $c{{m}^{2}}$ can make a total area of 9.375 ${{m}^{2}}$.
But the units of the total area is ${{m}^{2}}$.
We have to convert the total area in units of sq. cm.
We know that 1 m = 100 cm. We will square both sides.
1 ${{m}^{2}}$ = 10000 $c{{m}^{2}}$
Thus, 9.375 ${{m}^{2}}$ = 9.375 $\times $ 10000 $c{{m}^{2}}$
9.375 ${{m}^{2}}$ = 93750 $c{{m}^{2}}$
Now, to find the number of bricks that can be painted, we need to find the quotient of the total area that can be painted and the surface area of a single brick.
$\Rightarrow $ No of bricks = $\dfrac{93750\ c{{m}^{2}}}{937.5\ c{{m}^{2}}}$
$\Rightarrow $ No of bricks = 100.

Hence, 100 bricks can be painted with the available paint.

Note: In the unitary method, if we know the value of one unit, we can find the value of n units and this can be tweaked to suit our requirements. The condition is that all the units must be the same. Students are advised to be careful while unit conversion.