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EEJ MAIN Aptitude QUESTION #10932
Question 1
A right circular cone has a base radius of 7 cm and slant height of 25 cm. If it is unrolled to form a flat sector, what is the angle of the sector?
  • \(50.4°\
  • \(100.8°\✔️
  • \(75.6°\
  • \(201.6°\
Correct Answer Explanation

When a cone is unrolled, it forms a sector with:

  • Radius of sector = slant height = 25 cm
  • Arc length of sector = circumference of base = \(2\pi r = 2\pi \times 7 = 14\pi\ \text{cm}\

Angle of sector: \(\theta = \dfrac{\text{arc length}}{\text{radius}} = \dfrac{14\pi}{25}\ \text{radians}\

In degrees: \(\theta = \dfrac{14\pi}{25} \times \dfrac{180}{\pi} = \dfrac{14 \times 180}{25} = \dfrac{2520}{25} = 100.8°\

Wait — that gives 100.8°. The answer is option B (100.8°). Correcting: answer index should be 1.