The paint in a certain container is sufficient to paint an area equal to `10.2850m^2.` How many bricks of dimension `"21.5 cm "xx" 10 cm "xx "9.5 cm"` can be painted, out of this container?

Answer

To solve the problem, we need to determine how many bricks can be painted with the given amount of paint. We will follow these steps:

### Step 1: Calculate the total surface area of one brick

The dimensions of the brick are given as:
- Length (L) = 21.5 cm
- Breadth (B) = 10 cm
- Height (H) = 9.5 cm

The formula for the total surface area (A) of a cuboid is:
\[ A = 2(LB + BH + HL) \]

Substituting the values:
\[ A = 2(21.5 \times 10 + 10 \times 9.5 + 9.5 \times 21.5) \]

Calculating each term:
- \( LB = 21.5 \times 10 = 215 \, \text{cm}^2 \)
- \( BH = 10 \times 9.5 = 95 \, \text{cm}^2 \)
- \( HL = 9.5 \times 21.5 = 204.25 \, \text{cm}^2 \)

Now, adding these areas together:
\[ A = 2(215 + 95 + 204.25) \]
\[ A = 2(514.25) \]
\[ A = 1028.5 \, \text{cm}^2 \]

### Step 2: Convert the surface area of one brick from cm² to m²

To convert cm² to m², we use the conversion factor:
\[ 1 \, \text{cm}^2 = \frac{1}{10,000} \, \text{m}^2 \]

Thus, we convert:
\[ A = \frac{1028.5}{10,000} = 0.10285 \, \text{m}^2 \]

### Step 3: Calculate the number of bricks that can be painted

The total area that can be painted with the paint is given as:
\[ \text{Total area} = 10.2850 \, \text{m}^2 \]

To find the number of bricks that can be painted, we divide the total area by the area of one brick:
\[ \text{Number of bricks} = \frac{\text{Total area}}{\text{Area of one brick}} \]
\[ \text{Number of bricks} = \frac{10.2850}{0.10285} \]

Calculating this gives:
\[ \text{Number of bricks} = 100 \]

### Final Answer:
The number of bricks that can be painted is **100**.

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