The figure shows a cubic vessel of side 10 cm with water of depth 6 cm. A metal cuboid with a square base of side 5 cm and height 18 cm is put vertically into the vessel and no wat... The figure shows a cubic vessel of side 10 cm with water of depth 6 cm. A metal cuboid with a square base of side 5 cm and height 18 cm is put vertically into the vessel and no water spills out. Find the rise in the water level.

Understand the Problem
The question describes a scenario where a metal cuboid is placed into a cubic vessel filled with water. We need to determine how much the water level rises as a result of the cuboid being submerged.
Answer
$4.5$ cm
Answer for screen readers
The rise in the water level is $4.5$ cm.
Steps to Solve
- Calculate the volume of the cuboid submerged in water
The base of the cuboid is a square with side 5 cm, so the area of the base is $5 \times 5 = 25 \text{ cm}^2$. The cuboid is put vertically into the vessel and no water spills, this implies that the cuboid is fully submerged. Thus the height of the submerged portion is the height of the cuboid. The volume of the cuboid submerged in water is therefore $25 \times 18 = 450 \text{ cm}^3$.
- Calculate the area of the base of the cubic vessel
The base of the cubic vessel is a square with side 10 cm, so the area of the base is $10 \times 10 = 100 \text{ cm}^2$.
- Calculate the rise in water level
The volume of water displaced by the cuboid is equal to the volume of the cuboid submerged in the water, which is $450 \text{ cm}^3$. Let $h$ be the rise in the water level. The volume of the water that rises is equal to the area of the base of the vessel multiplied by the rise in water level, so we have: $100 \times h = 450$
Solving for $h$, we get: $h = \frac{450}{100} = 4.5 \text{ cm}$.
The rise in the water level is $4.5$ cm.
More Information
When an object is submerged in water, it displaces a volume of water equal to the volume of the submerged portion of the object. This displaced water causes the water level to rise in the vessel.
Tips
null
AI-generated content may contain errors. Please verify critical information