An open cone with base radius 28cm and perpendicular height 96cm was stretched to form sector of a circle…

Analyze the question: An open cone (curved surface only) is opened out flat into a sector. The question says "arc," but the options are in cm², so the intended quantity is almost certainly the area of the sector, which equals the curved surface area of the cone.

Concept:

• Slant height: l = √(r² + h²)
• Curved surface area of cone = πrl
• The sector's radius is l, and its arc length equals the base circumference 2πr.

Solution:

1. Slant height: l = √(28² + 96²) = √(784 + 9216) = √10000 = 100 cm

2. Curved surface area = area of sector: A = πrl = (22/7) × 28 × 100 = 22 × 4 × 100 = 8800 cm²

Check on "arc": The actual arc length would be 2πr = 2 × (22/7) × 28 = 176 cm, which is not among the options (and the options are in cm², not cm). So the question wording is faulty, and the answer that fits the options is the sector area, 8800 cm².

Option B (8448) would be π × 28 × 96, which wrongly uses the vertical height instead of the slant height. Option D (4224) is half of that. Option C (4400) is half of 8800, which comes from wrongly using ½πrl.

Answer: A. 8800 cm²

Tip: For cone problems, always find the slant height first. Look for Pythagorean triples: here 28:96:100 is 7:24:25 scaled by 4. Also, never use the vertical height in the curved surface area formula.