The paint in a certain container is sufficient to paint an area equal to `10.865 m^2` How many bricks of dimensions `31.5 cm xx 10 cm xx 5.5 cm` can be painted from that paint?

Options

A. 150
B. 200
C. 100
D. 250

Answer

To solve the problem, we need to find out how many bricks can be painted with the given amount of paint that can cover an area of 10.865 m².

**Step 1: Calculate the surface area of one brick.**

The brick has dimensions of 31.5 cm x 10 cm x 5.5 cm. We need to calculate the surface area of the brick.

The surface area (SA) of a rectangular brick can be calculated using the formula:
\[ SA = 2(lw + lh + wh) \]
where:
- \( l \) = length
- \( w \) = width
- \( h \) = height

Converting the dimensions from centimeters to meters:
- Length (l) = 31.5 cm = 0.315 m
- Width (w) = 10 cm = 0.1 m
- Height (h) = 5.5 cm = 0.055 m

Now, substituting the values into the surface area formula:
\[ SA = 2(0.315 \times 0.1 + 0.315 \times 0.055 + 0.1 \times 0.055) \]
Calculating each term:
- \( lw = 0.315 \times 0.1 = 0.0315 \)
- \( lh = 0.315 \times 0.055 = 0.017325 \)
- \( wh = 0.1 \times 0.055 = 0.0055 \)

Now summing these:
\[ SA = 2(0.0315 + 0.017325 + 0.0055) = 2(0.054325) = 0.10865 \, m^2 \]

**Step 2: Calculate how many bricks can be painted with the available paint.**

We know the total area that can be painted is 10.865 m². To find the number of bricks that can be painted, we divide the total paintable area by the surface area of one brick:
\[ \text{Number of bricks} = \frac{\text{Total paintable area}}{\text{Surface area of one brick}} = \frac{10.865}{0.10865} \]

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

Thus, approximately 100 bricks can be painted with the available paint.

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