A sphere with a radius of 9 cm is melted and cast into a cylinder with a radius of 3 cm. Find the height of that cylinder.

Appeared in: DSSSB - 28 August 2019 (Shift-1)

Explanation

The fundamental principle is that when an object is melted and recast, its volume remains constant.
The volume of the sphere is calculated as V = (4/3) × π × (9 cm)³ = 972π cm³.
The volume of the cylinder is V = π × (3 cm)² × h = 9πh cm³.
By equating the two volumes (972π = 9πh), we can solve for the height (h).
Dividing both sides by 9π gives h = 972π / 9π, which simplifies to h = 108 cm.

Option B: This value (216 cm) is double the correct answer. This error could occur by incorrectly multiplying by 2 at some stage, for instance, miscalculating 9³ as 729×2 or incorrectly simplifying the final division.
Option C: This value (54 cm) is half the correct answer. This might result from an arithmetic error, such as dividing by 2 incorrectly or making a mistake in the volume calculation, for example, forgetting the (4/3) factor in the sphere's volume formula and using only r³.
Option D: This value (162 cm) could be the result of a calculation mistake, such as confusing the radii or making an error in cubing or squaring the numbers. For example, if one incorrectly calculated (4/3) * 9³ / 3².

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Conservation of Volume and Geometric Formulas as background academic context rather than a clinical decision trigger.
This question is from the non-nursing subject of mathematics, often included in nursing entrance exams to assess general aptitude.
It tests the candidate's ability to apply mathematical formulas and use logical reasoning to solve problems.
Strong analytical and problem-solving skills are valuable in nursing for tasks like medication dosage calculations and interpreting patient data.

How to Approach the Question

First, identify the core principle of the question: an object is being reshaped, which means its volume is conserved.
Recall the correct mathematical formulas for the volumes of the shapes involved: a sphere (V = 4/3 × π × r³) and a cylinder (V = π × r² × h).
Set up an equation where the volume of the sphere is equal to the volume of the cylinder.
Substitute the known values (radius of the sphere and radius of the cylinder) into the equation.
Algebraically rearrange the equation to isolate the unknown variable, which is the height (h) of the cylinder.
Perform the calculations carefully to find the final numerical answer and compare it with the given options.

Concept Tested & Keywords

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Practise the full DSSSB - 28 August 2019 (Shift-1)

Attempt every question from this paper in a timed mock, then review the full solution for each one.