A cone of maximum volume is inscribed in a given sphere, th…

Maths Differentiation and Applications of Derivatives Maxima and Minima Single Correct MCQ

Published on: August 13, 2026

A cone of maximum volume is inscribed in a given sphere, then ratio of the height of the cone to diameter of the sphere is

2/3

3/4

1/3

1/4

Text Solution

Verified by Experts

The correct answer is:

Let diameter of sphere

Let radius of cone is x and height is y

∴ ∴ , since

or ……(i)

Volume of cone

⇒ ⇒ ⇒ ⇒

⇒ ⇒ ⇒ ⇒ ⇒ ⇒

Now , put

⇒ ⇒ = negative value

So, volume of cone is maximum at

⇒ ⇒ = .

Previous Question Next Question

Get practice questions, solutions, and test series in one place.

Share your experience with this question and solution.

Send your comment, doubt, correction, or feedback to admin.

What students say about this solution

No reviews yet. Be the first to write a review.