Question

The paint in a container is sufficient to paint an area equal to \[18.72{\text{ }}{{\text{m}}^2}\]. How many tiles of dimension \[24{\text{ cm}} \times 18{\text{ cm}} \times 12{\text{ cm}}\] can be painted by this paint.

Answer 1

Hint: Here, we will use the formula of total surface area of cuboid \[2\left( {lb + bh + hl} \right)\], where \[l\] is the length, \[b\] is the base and \[h\] is the height and then divide this area of the tiles with the total area.

Complete step-by-step solution:
It is given that the total area is \[18.72{\text{ }}{{\text{m}}^2}\].
We know that the total surface area of each tile is \[2\left( {lb + bh + hl} \right)\], where \[l\] is the length, \[b\] is the base and \[h\] is the height.

We will now find the values of \[l\], \[b\] and \[h\].

\[l = 24\]
\[b = 18\]
\[h = 12\]

Substituting these values in formula of total surface area \[2\left( {lb + bh + hl} \right)\], we get

\[
  {\text{Total surface area of each tile}} = 2\left( {24 \times 18 + 18 \times 12 + 12 \times 24} \right) \\
   = 2\left( {432 + 216 + 288} \right) \\
   = 2\left( {936} \right) \\
   = 1872{\text{ c}}{{\text{m}}^2} \\
\]

We will now convert the total area \[18.72{\text{ }}{{\text{m}}^2}\] into centimeters.

\[18.72 \times {10^4}{\text{ c}}{{\text{m}}^2}\]

Now we will calculate the number of tiles by dividing the total area by the total surface area of each tile.

\[
  {\text{No. of tiles}} = \dfrac{{18.72 \times {{10}^4}{\text{ }}}}{{1872}} \\
   = \dfrac{{187200}}{{1872}} \\
   = 100 \\
\]

Thus, 100 tiles of the given dimension can be painted by this paint.

Note: In this question, students should know the formula of total surface area of cone and conversion of meters into centimeters. Also, we are supposed to write the values properly to avoid any miscalculation.