Multiple choice

A solid metallic prism whose area of base is 126 cm2 and height is 77cm is melted and recast in the shape of a cone if the radius and height of cone is equal then find the radius of cone. एक ठोस धात्विक प्रिज्म जिसके आधार का क्षेत्रफल 126 सेमी2 और ऊचाई 77 सेमी. है ,को पिघलाकर उसे पुनः एक शंकु के आकार में ढाला जाता है ,जिसकी आधार त्रिज्या और ऊचाई बराबर है। तो शंकु की त्रिज्या ज्ञात कीजिये ।

  1. 21 cm/सेमी.

  2. 14 cm/सेमी.

  3. 28 cm/सेमी.

  4. 3.5 cm/सेमी.

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of prism = Base area × height = 126 × 77 = 9702 cm³. This equals volume of cone = (1/3)πr²h. Given r = h for the cone, so (1/3)πr³ = 9702. Using π = 22/7: (1/3)(22/7)r³ = 9702, giving r³ = 9702 × 21/22 = 441 × 21 = 9261. Therefore r = ³√9261 = 21 cm. Option A matches. The key is equating volumes and using r = h.