Question

The paint in a containe is sufficient to paint an area equal to 3.96m^2. How many cuboid boxes measuring 15cm by 12cm by 8cm can be painted with the point in this container?​

Answer 1

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Given: Dimensions of the brick 22.5cm × 10cm × 7.5cm

Since brick is cuboidal in shape, the surface area of the brick will be the total surface area of the cuboid.

Hence, the area of each brick to be painted will be the total surface area of the cuboid

Total surface area of cuboid = 2(lb + bh + hl)

The paint in a certain container is sufficient to paint an area equal to 9.375m2. How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?

The number of bricks that can be painted out of the container can be calculated by dividing the area which can be painted with paint available in the container by the area of each brick.

The area which can be painted with the paint available in the container = 9.375m2.

Let the length, breadth, and height of the bricks be l, b, and h respectively.

l = 22.5 cm

b = 10 cm

h = 7.5 cm

The area of each brick to be painted = 2(lb + bh + hl)

2(lb + bh + hl) = 2 × (22.5 cm × 10 cm + 10 cm × 7.5 cm + 7.5 cm × 22.5 cm)

= 2 × (225 cm2 + 75 cm2 + 168.75 cm2)

= 2 × 468.75 cm2

= 937.5 cm2

Number of bricks that can be painted = The area which can be painted with the paint available in the container / The area of each brick

= 9.375 m2 / 937.5 cm2

= (9.375 × 10000 cm2) / 937.5 cm2 [since 1m2 = 10000cm2]

= 100

Thus, the number of bricks that can be painted out of the container is 100.