The volume of a solid cylinder is 40194 cm³ and its height is 29 cm. What is the total surface area of the solid cylinder? (Nearest to an integer)

Appeared in: RRB Nsg. Superintendent -29 April-2025 (shift-2nd)

Explanation

The solution involves a two-step process: first calculating the radius from the given volume and height, and then using that radius to find the total surface area.
The formula for the volume of a cylinder is V = πr²h. By substituting the given volume (40194 cm³) and height (29 cm), the radius (r) is calculated to be 21 cm.
The formula for the total surface area of a cylinder is TSA = 2πr(r + h), which includes the area of the top and bottom circular faces plus the curved surface area.
Substituting r = 21 cm and h = 29 cm into the TSA formula yields 2 × (22/7) × 21 × (21 + 29), which simplifies to 6600 cm².

Option A: This value is incorrect and likely results from a miscalculation during the multiplication or division steps when finding either the radius or the final surface area.
Option B: This value is incorrect. It may arise from an arithmetic error, such as incorrectly summing the radius and height before multiplying.
Option D: This value is incorrect. This could be the result of a calculation mistake, possibly in the final multiplication step to determine the total surface area.

Visual 1: Diagram - A labeled diagram of a solid cylinder, clearly showing the radius (r) of the circular base and the height (h) of the cylinder. This helps visualize the components used in the formulas.
Visual 2: Flowchart - A flowchart illustrating the two-step problem-solving process: 1. Use Volume and Height to find Radius. 2. Use Radius and Height to find Total Surface Area.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Mensuration - Properties of a Solid Cylinder as background academic context rather than a clinical decision trigger.
This is a general aptitude and reasoning question, not a clinical one.
Quantitative aptitude questions are included in nursing entrance exams to assess a candidate's problem-solving skills, logical reasoning, and ability to perform calculations accurately, which are essential skills in a clinical setting for tasks like medication dosage calculation.
What if the question asked for the curved surface area instead? The formula would be CSA = 2πrh. The calculation would be 2 × (22/7) × 21 × 29 = 3828 cm². This highlights the importance of carefully reading the question to apply the correct formula.

How to Approach the Question

First, identify all the given information in the problem: the volume of the cylinder is 40194 cm³ and its height is 29 cm.
Next, determine what needs to be calculated: the total surface area (TSA) of the cylinder.
Recall the formula for the volume of a cylinder: V = πr²h. Realize that you can use the given volume and height to solve for the unknown radius (r).
Rearrange the volume formula to solve for r²: r² = V / (πh). Substitute the values and calculate r.
Once the radius is found, recall the formula for the total surface area of a cylinder: TSA = 2πr(r + h).
Substitute the calculated radius (r) and the given height (h) into the TSA formula and compute the final answer.

Concept Tested & Keywords

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Practise the full RRB Nsg. Superintendent -29 April-2025 (shift-2nd)

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