Question

a cuboid of dimensions 8cm x 5 cm x 6 cm is placed in water such that the 8 cm side is vertical. it floats with 2 cm (of the 8 cm side) above the water surface. if the same cuboid is now placed with the 6 cm side vertical, how much of its height will be above the water surface?

Answer 1

When the cuboid is placed with the 6 cm side vertical, the entire 6 cm of its height will be above the water surface.

Step-by-step explanation:

When a cuboid is placed in water, it will float if it is less dense than the water. In this case, the cuboid floats with 2 cm of the 8 cm side above the water surface.

The amount of the height that will be above the water surface when the cuboid is placed with the 6 cm side vertical can be determined using the principle of flotation.

The volume of the cuboid remains the same, so the height that will be above the water surface can be obtained by rearranging the formula for the volume of a cuboid.

Let's calculate it:

Given dimensions of the cuboid: 8 cm x 5 cm x 6 cm

1. Volume of the cuboid = length x width x height
2. Volume = 8 cm x 5 cm x 6 cm = 240 cm³
3. When the 6 cm side is vertical, the height of the cuboid is 6 cm.
4. Using the formula for volume of a cuboid, we can rearrange it to solve for height: Height = Volume / (length x width)
5. Height = 240 cm³ / (8 cm x 5 cm) = 6 cm

Therefore, when the cuboid is placed with the 6 cm side vertical, the entire 6 cm of its height will be above the water surface.