Multiple choice

Find the surface area of largest possible sphere inscribed in a cone of radius 21 cm and slant height equal to the diameter of the base. 21 सेमी.त्रिज्या के एक शंकु के अंर्तगत, जिसकी तिर्यक ऊँचाई उसके आधार के व्यास के बराबर है, गोले का पृष्ठीय क्षेत्रफल ज्ञात कीजिये।

  1. 1650 cm2/सेमी.2

  2. 1830 cm2/सेमी.2

  3. 1848 cm2/सेमी.2

  4. 1770 cm2/सेमी.2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Cone: radius r=21, slant height l=2r=42, so height h=√(l²-r²)=21√3. Inscribed sphere touches base and sides. Largest inscribed sphere has radius R = r×h/(r+√(r²+h²)) = 21×21√3/(21+42) = 7√3. Surface area = 4πR² = 4π×147 = 1848. Answer C is correct.

Keep practicing — related questions