Question

The paint in a certain container is sufficient to paint an area equal to $9.375{\text{ }}{{\text{m}}^2}$. Bricks of dimension $22.5{\text{ cm }} \times {\text{ 10 cm }} \times {\text{ 7}}{\text{.5 cm}}$ are to be painted. The number of bricks that can be painted is
$
  {\text{a}}{\text{. 200}} \\
  {\text{b}}{\text{. 100}} \\
  {\text{c}}{\text{. 150}} \\
  {\text{d}}{\text{. 50}} \\
$

Answer 1

Hint: Surface area of one brick is given as $2\left( {lb + bh + hl} \right)$ use this property to reach the answer. Where symbols have their usual meaning.

Complete step by step solution:
Given data
Dimension of the brick is $22.5{\text{ cm }} \times {\text{ 10 cm }} \times {\text{ 7}}{\text{.5 cm}}$
So, length (l) of brick is 22.5 cm
Breath (b) of brick is 10 cm
Height (h) of brick is 7.5 cm
Now we know that the surface area of the brick is given as $2\left( {lb + bh + hl} \right)$
So, calculate the surface area (S.A) of one brick $2\left( {\left( {22.5 \times 10} \right) + \left( {10 \times 7.5} \right) + \left( {7.5 \times 22.5} \right)} \right)$
$S.A = 2\left( {225 + 75 + 168.75} \right) = 937.50{\text{ c}}{{\text{m}}^2}$
Now, it is given that the paint in a certain container is sufficient to paint an area (A) equal to $9.375{\text{ }}{{\text{m}}^2}$.
Now we know that $1{\text{ m = 100 cm}}$
$ \Rightarrow A = 9.375 \times {\left( {100{\text{ cm}}} \right)^2} = 9.375 \times 10000{\text{ c}}{{\text{m}}^2} = 93750{\text{ c}}{{\text{m}}^2}$.
Therefore number of bricks (B) $ = \dfrac{{{\text{Area to be painted}}}}{{{\text{Surface area of 1 brick}}}}$
$ \Rightarrow B = \dfrac{{93750}}{{937.50}} = 100$
So, the number of bricks that can be painted is 100.
Hence option (b) is correct.

Note: In such types of questions first calculate the surface area of one brick then convert the S.I unit of area to be painted into sq.cm using unit conversion as above then divide this area from the surface area of one brick, so it gives us the required number of bricks that can be painted.