A cylindrical tank with radius r meters and height h meters is filled with water. A solid metallic cylinder of radius 1/2 and height 2h is submerged completely in the tank. By what fraction does the water level in the tank rise?

1. A

   1/16

2. B

   1/2

3. C

   1/8

4. D

   1/4

Appeared in: RRB Nsg. Superintendent-2026 (Shift -1st)

Explanation

• The core principle is that the volume of water displaced is equal to the volume of the submerged object.
• First, calculate the volume of the submerged solid cylinder: V_solid = π × (radius)² × height = π × (r/2)² × 2h = (πr²h)/2.
• This displaced volume (V_solid) causes the water level in the main tank to rise. The volume of the rise is (Base Area of Tank) × (height of rise, x) = (πr²) × x.
• Equating the volumes: (πr²h)/2 = (πr²) × x.
• Solving for the rise in height 'x' gives x = h/2.
• The question asks for this rise as a fraction. Comparing the rise (h/2) to the tank's height (h), the fraction is (h/2) / h = 1/2.

Why Other Options Were Wrong

• Option A: A fraction of 1/16 is incorrect. This result would be obtained if the submerged cylinder had a height of h/8, not 2h.
• Option C: A fraction of 1/8 is incorrect. This error arises if one incorrectly calculates the volume of the submerged cylinder, for instance, by using a height of h/2 instead of 2h.
• Option D: A fraction of 1/4 is incorrect. This common error occurs if the height of the submerged cylinder is mistakenly taken as 'h' instead of the given '2h'.

Related Visual

• Visual 1: Diagram - A two-panel diagram. The first panel shows a cylinder with radius 'r' filled with water to a height 'h'. The second panel shows the same cylinder with a smaller cylinder (radius r/2, height 2h) fully submerged, and the water level risen by a height 'x', where x = h/2.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Fluid Displacement and Volume of a Cylinder as background academic context rather than a clinical decision trigger.
• This is a mathematics question testing principles of geometry and physics, not clinical nursing.
• The underlying principle of volume displacement is relevant in some advanced medical measurements, such as hydrostatic weighing (underwater weighing) to determine body composition and density.
• What if the submerged cylinder was hollow and open at the top? If it filled with water, it would displace a volume of water equal to the volume of the material it's made of, which would be much less than its total volume, leading to a significantly smaller rise in water level.

How to Approach the Question

• First, identify all the given parameters: the dimensions of the tank (radius r, height h) and the dimensions of the submerged object (radius r/2, height 2h).
• Recall the formula for the volume of a cylinder: V = π × r² × h.
• Calculate the volume of the object being submerged. This volume is equal to the volume of the fluid that will be displaced.
• Set up an equation for the volume of the displaced fluid within the main container. This volume is the base area of the container multiplied by the unknown rise in height (x).
• Equate the volume of the submerged object with the volume of the displaced fluid and solve for the rise in height (x).
• Finally, express the rise (x) as a fraction of the reference height (h) to match the format of the options.

Concept Tested & Keywords

• Concept Tested: Fluid Displacement and Volume of a Cylinder
• Stem keywords: cylindrical tank, radius, height, submerged, water level, fraction
• Lead-in keywords: By what fraction

Question ID

QNKnyVaCVHUVLgQ3hNm6gu

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