The perimeter of the base of a right circular cone is 16π cm. If the height of the cone is 48 cm, then its volume is:

Appeared in: DSSSB October 2024

Explanation

The solution requires a two-step process: first determining the radius of the cone's base and then calculating the volume.
The radius (r) is found using the formula for the perimeter (circumference) of a circle, C = 2πr. Given C = 16π cm, the radius is calculated to be 8 cm.
The volume (V) is then calculated using the formula V = (1/3)πr²h.
Substituting the known values, r = 8 cm and h = 48 cm, into the volume formula gives V = (1/3) × π × (8)² × 48.
Simplifying the expression results in V = 1024π cm³, which is the correct volume.

Option B: This value is incorrect. It might result from a calculation error, such as using an incorrect height.
Option C: This value is mathematically incorrect and does not correspond to the given dimensions. It is likely a result of a significant calculation error.
Option D: This value is also mathematically incorrect. It likely stems from an error in applying the volume formula or an arithmetic mistake during calculation.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the volume of a right circular cone from its base perimeter and height as background academic context rather than a clinical decision trigger.
This question assesses foundational mathematical skills in geometry and mensuration, which are part of the general aptitude section of nursing exams.
Strong numerical ability is essential for nurses for tasks like medication dosage calculations, interpreting vital signs charts, and managing fluid balances.
What if the question provided the base area instead of the perimeter? If the area (A = πr²) was given, you would first solve for the radius (r = √A/π) and then proceed to calculate the volume with the same volume formula.

How to Approach the Question

First, identify the given information in the problem: the perimeter of the base (16π cm) and the height of the cone (48 cm).
Next, determine what needs to be calculated: the volume of the cone.
Recall the formula for the perimeter (circumference) of a circle: C = 2πr. Use the given perimeter to solve for the radius (r) of the cone's base.
Once the radius is known, recall the formula for the volume of a cone: V = (1/3)πr²h.
Substitute the calculated radius and the given height into the volume formula.
Perform the calculation carefully to find the final volume and compare your result with the given options.

Concept Tested & Keywords

Concept Tested: Calculating the volume of a right circular cone from its base perimeter and height.
Stem keywords: right circular cone, perimeter of the base, height, volume
Lead-in keywords: then its volume is

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