Question

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

Answer 1

Step 1: Calculate the total surface area of the brick

The dimension of the brick is given as $22.5cm\times 10cm\times 7.5cm$.

The total surface area of a cuboid with length $l$, width $w$ and height $h$ can be given by, $2\left(lw+wh+lh\right)$.

Thus the total surface area of the given cuboid can be given by,

$$\begin{gathered} =2\left[\left(22.5\times 10\right)+\left(10\times 7.5\right)+\left(22.5\times 7.5\right)\right] \\ =2\left[225+75+168.75\right] \\ =2\times 468.75 \\ =937.5c{m}^2 \\ =\frac{937.5}{{\left(100\right)}^2}{m}^2 \\ =0.09375m^2 \end{gathered}$$

Therefore, the total surface area of the brick is $0.09375m^2$.

Step 2: Calculate the number of bricks that can be painted by one paint container.

It is given that the paint container is sufficient to paint an area equal to $9.375m^2$.

Thus the number of bricks with an area of $0.09375m^2$ can be painted by the container is $\frac{9.375m^2}{0.09375m^2}=100$.

Hence, the number of bricks with the dimensions $22.5cm\times 10cm\times 7.5cm$ can be painted out of this container is$100$.