A right circular cone has a radius of 7 cm and height of 24 cm. What is the slant height?

Question

A right circular cone has a radius of 7 cm and height of 24 cm. What is the slant height?

1. A. 25 cm (Correct answer)
2. B. 30 cm
3. C. 35 cm
4. D. 40 cm

Correct Answer

Option A — 25 cm

Detailed Solution & Explanation

The correct answer is 25 cm.

Key Points

• The radius, height and slant height of a right circular cone form a right triangle, so l² = r² + h².
• Substituting: l² = 7² + 24² = 49 + 576 = 625, giving l = 25 cm.
• (7, 24, 25) is a standard Pythagorean triple; recognising it removes the arithmetic entirely.
• Related cone formulae worth keeping together: curved surface area = πrl, total surface area = πr(l + r) and volume = (1/3)πr²h.
• Other triples that recur in mensuration: (3, 4, 5), (5, 12, 13), (8, 15, 17) and (9, 40, 41).

Additional Information

• Cone formulae: slant height l = √(r² + h²), curved surface area = πrl, total surface area = πr(l + r) and volume = (1/3)πr²h.
• A cone's volume is exactly one-third of the cylinder with the same base and height — a relation frequently tested directly.
• Pythagorean triples worth recognising on sight: (3,4,5), (5,12,13), (7,24,25), (8,15,17), (9,40,41) and (20,21,29), along with their multiples.

प्रश्न (हिन्दी में)

एक लम्ब वृत्तीय शंकु की त्रिज्या 7 सेमी और ऊँचाई 24 सेमी है। तिर्यक ऊँचाई क्या है?

1. A. 25 सेमी
2. B. 30 सेमी
3. C. 35 सेमी
4. D. 40 सेमी