The slant height of a right circular cone is 25 cm and the height is 20 cm. What is the total surface area of the cone? (in cm², taking π = 3.14)

Appeared in: DSSSB - 29 August 2019 (Shift-1)

Explanation

The first step is to calculate the radius (r) of the cone's base, as it is not provided directly.
Using the Pythagorean theorem (l² = r² + h²), the radius is found: r = √(l² - h²) = √(25² - 20²) = √225 = 15 cm.
The formula for the Total Surface Area (TSA) of a cone is TSA = πr(r + l), which includes the area of the circular base and the curved surface.
Substituting the known values (r=15 cm, l=25 cm, π=3.14) into the formula gives: TSA = 3.14 × 15 × (15 + 25).
The final calculation is 3.14 × 15 × 40, which equals 1884 cm².

Option A: This value is incorrect and likely results from a miscalculation during the multiplication steps.
Option C: This value is incorrect. It might arise from an arithmetic error, such as incorrectly multiplying 3.14 by 600.
Option D: This value is incorrect. It is close to the correct answer and could be the result of a minor calculation error or rounding difference.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Mensuration: Total Surface Area of a Cone as background academic context rather than a clinical decision trigger.
This is a mathematical question designed to test skills in geometry and mensuration.
There is no direct clinical application or nursing action related to calculating the surface area of a cone.
What if? - If the stem changed one defining clue so that 1884 cm² no longer matched, reassess the option whose mechanism, classification, or indication now fits the revised presentation.

How to Approach the Question

First, identify all the given parameters from the question: slant height (l = 25 cm) and height (h = 20 cm).
Recognize that the formula for Total Surface Area (TSA) of a cone, TSA = πr(r + l), requires the radius (r), which is not given.
Use the relationship between slant height, height, and radius in a right circular cone (Pythagorean theorem: l² = r² + h²) to calculate the missing radius.
Substitute the calculated radius and the given slant height and π value into the TSA formula.
Perform the arithmetic calculation carefully (3.14 × 15 × 40) to arrive at the final answer.
Match the calculated result with the given options to select the correct one.

Concept Tested & Keywords

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Practise the full DSSSB - 29 August 2019 (Shift-1)

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