The paint in a certain container is sufficient to paint an darea equal to `9.375 m^(2)`. How many bricks measuring 22.5 cm by 10 cm by 75 cm can be painted out of this container ?

Options

A. 200
B. 1000
C. 10
D. 100

Answer

To solve the problem of how many bricks can be painted with the given paint, we will follow these steps:

### Step 1: Convert the area that can be painted from square meters to square centimeters.
The area that can be painted is given as \(9.375 \, m^2\). We know that \(1 \, m^2 = 10,000 \, cm^2\).

\[ \text{Area in } cm^2 = 9.375 \, m^2 \times 10,000 \, cm^2/m^2 = 93,750 \, cm^2 \]

### Step 2: Calculate the total surface area (TSA) of one brick.
The dimensions of the brick are given as:
- Length (\(l\)) = 22.5 cm
- Breadth (\(b\)) = 10 cm
- Height (\(h\)) = 7.5 cm

The formula for the total surface area of a cuboid is:

\[ \text{TSA} = 2(lb + bh + hl) \]

Substituting the values:

\[ \text{TSA} = 2(22.5 \times 10 + 10 \times 7.5 + 22.5 \times 7.5) \]

Calculating each term:

\[ = 2(225 + 75 + 168.75) = 2(468.75) = 937.5 \, cm^2 \]

### Step 3: Determine how many bricks can be painted.
To find the number of bricks that can be painted, we divide the total area that can be painted by the surface area of one brick:

\[ \text{Number of bricks} = \frac{\text{Total area}}{\text{Area of one brick}} = \frac{93,750 \, cm^2}{937.5 \, cm^2} \]

Calculating this gives:

\[ = 100 \]

### Conclusion:
Thus, the number of bricks that can be painted with the paint in the container is **100**.

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