Question

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

Answer 1

Step 1. Calculate the surface area of bricks.

First, need to convert the area $9.375{\mathrm{m}}^2$ into ${\mathrm{cm}}^2$.

$$\begin{gathered} 9.375{\mathrm{m}}^2=9.375\times {(100\mathrm{cm})}^2 \\ =93750{\mathrm{cm}}^2 \end{gathered}$$

Since the dimension of a brick is $22.5\times 10\times 7.5\mathrm{cm}$.

$$\begin{gathered} \mathrm{Total}\mathrm{surface}\mathrm{area}=2(lb+bh+hl) \\ =2(22.5\times 10+10\times 7.5+22.5\times 7.5) \\ =2(225+75+168.75) \\ =2\times 468.75 \\ =937.5{\mathrm{cm}}^2 \end{gathered}$$

Step 2. Calculate the number of bricks.

The number of bricks $\left(n\right)$ can be computed as:

$$\begin{gathered} n=\frac{\mathrm{Area}\mathrm{painted}\mathrm{by}\mathrm{the}\mathrm{container}}{\mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{brick}} \\ =\frac{93750}{937.5} \\ =100 \end{gathered}$$

Hence, the number of bricks is $100$.