The volume of a solid cylinder is 80, 850 cm3 and its height is 21c& x6D; . Find the total surface area of the cylinder. (Use pi \=. 22/7

RRB Nsg. Superintendent-2026 (Shift -2nd)

Non Nursing Subjects

Hard

The volume of a solid cylinder is 80,850 cm3 and its height is 21cm. Find the total surface area of the cylinder.
(Use pi=. 22/7

Appeared in: RRB Nsg. Superintendent-2026 (Shift -2nd)

The solution involves a two-step process: first finding the radius from the given volume and height, then using the radius to calculate the total surface area.
Using the volume formula V = πr²h, the radius (r) is calculated. Given V = 80,850 cm³ and h = 21 cm, we get 80,850 = (22/7) × r² × 21, which simplifies to r² = 1225, so r = 35 cm.
Next, the total surface area (TSA) is found using the formula TSA = 2πr(r + h).
Substituting the values r = 35 cm and h = 21 cm, we get TSA = 2 × (22/7) × 35 × (35 + 21) = 2 × 22 × 5 × 56 = 12,320 cm².

Option A: This value is incorrect. It may arise from a miscalculation, such as an error in finding the radius or during the final multiplication for the total surface area.
Option B: This value is incorrect. It represents a calculation error, possibly in summing the radius and height or in the final multiplication step.
Option D: This value is incorrect. It is close to the correct answer but likely results from a minor arithmetic mistake during the calculation process.

Visual 1: Diagram - An annotated diagram of a solid cylinder, clearly labeling the radius (r), height (h), the circular top and bottom surfaces (area = πr² each), and the curved side surface (area = 2πrh).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the total surface area of a solid cylinder using its volume and height as background academic context rather than a clinical decision trigger.
This question assesses fundamental mathematical and problem-solving skills, which are essential for various calculations in healthcare, such as dosage calculations, fluid balance monitoring, and interpreting quantitative data.
While not a direct clinical scenario, the logical reasoning and precision required to solve this problem are transferable to the meticulous nature of nursing practice.
What if the question asked for the curved surface area instead? The formula would be 2πrh, which would be 2 × (22/7) × 35 × 21 = 4620 cm². This highlights the importance of carefully reading the question to apply the correct formula.

How to Approach the Question

First, identify the given information: the volume of the cylinder (80,850 cm³) and its height (21 cm). Also, note the value of π to be used (22/7).
Recognize 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 this formula to find the radius (r), which is the missing piece of information needed for the TSA calculation.
Substitute the given values into the volume formula and solve for 'r'.
Once the radius is found, recall the formula for the total surface area of a solid cylinder: TSA = 2πr(r + h).
Substitute the now-known values of r, h, and π into the TSA formula and perform the calculation carefully.

Concept Tested & Keywords

Concept Tested: Calculating the total surface area of a solid cylinder using its volume and height.
Stem keywords: volume of a solid cylinder, height, total surface area
Lead-in keywords: What is

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