If the height of a right circular cylinder is 14 cm and its curved surface area is 704 cm², then its volume w… - ESIC Nursing Officer - 2019 (Shift-2)

ESIC Nursing Officer - 2019 (Shift-2)

Non Nursing Subjects

Hard

Appeared in: ESIC Nursing Officer - 2019 (Shift-2)

Explanation

The core task is to first find the cylinder's radius using the given curved surface area (CSA) and height, and then use that radius to calculate the volume.
The formula for CSA is 2 * π * r * h. Plugging in the given values (CSA = 704 cm², h = 14 cm), we can solve for the radius (r).
704 = 2 * (22/7) * r * 14, which simplifies to 704 = 88 * r. Solving for r gives r = 8 cm.
The formula for volume is π * r² * h. Using the calculated radius (r = 8 cm) and given height (h = 14 cm), we get the volume.
Volume = (22/7) * (8)² * 14, which calculates to 2816 cm³.

Option A: This value (1408 cm³) is exactly half of the correct volume. This error could occur if a factor of 2 was missed during the volume calculation (e.g., calculating 22 * 64 instead of 22 * 64 * 2).
Option B: This value (5632 cm³) is exactly double the correct volume. This might result from an arithmetic error, such as incorrectly multiplying the final result by 2.
Option C: This value (9856 cm³) does not correspond to a simple calculation error based on the given numbers. It is significantly larger than the correct volume.

Visual 1: Diagram - A labeled diagram of a right circular cylinder, clearly showing the radius (r) at the circular base and the height (h) as the perpendicular distance between the bases. This helps visualize the dimensions used in the formulas.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Mensuration - Volume of a Cylinder as background academic context rather than a clinical decision trigger.
This question tests general aptitude and mathematical skills, which are part of the non-nursing section of nursing entrance exams.
Strong foundational math skills are essential for nurses for tasks like medication dosage calculation, IV drip rate regulation, and interpreting patient data charts, ensuring patient safety.
What if the question asked for the Total Surface Area (TSA)? You would first find the radius (r=8 cm) as done in Step 1, then use the TSA formula: TSA = 2 * π * r * (h + r) = 2 * (22/7) * 8 * (14 + 8) = 1106.28 cm².

How to Approach the Question

First, identify all the given information in the problem: height (h = 14 cm) and curved surface area (CSA = 704 cm²).
Next, identify what you need to find: the volume (V) of the cylinder.
Recall the relevant formulas. You'll need the formula for CSA (2 * π * r * h) and the formula for Volume (π * r² * h).
Notice that the volume formula requires the radius (r), which is not given directly. Use the CSA formula and the given values to solve for the unknown radius.
Once you have calculated the radius, substitute it and the given height into the volume formula.
Perform the final calculation carefully to find the volume and match your result with the given options.

Concept Tested & Keywords

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