JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 26 June 2022, Shift 2, Maths Q6

Question 6 of 90 in this shift, Maths question 6 of 30, Section A.

Cosider a cuboid of sides

2x

4x

and

5x

and a closed hemisphere of radius

r

. If the sum of their surface areas is a constant

k

, then the ratio

x : r

, for which the sum of their volumes is maximum, is :

(1) $2:5$
(2) $19:45$ Official answer
(3) $3:8$
(4) $19:15$

Official answer

Option 2

NTA final key.

Chapter: Application of Derivatives
Topic: Maxima and Minima
Idea tested: Optimization Problems

Same idea in other shifts

Asked 13× in all

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.