# Finding largest volume of right circular cone inscribed in a sphere of radius 3

Discussion in 'Calculus' started by Eulers_Disciple, Sep 6, 2023.

1. ### Eulers_Disciple

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Sep 6, 2023
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I would like some assistance solving the applied optimization problem in my my calculus book that ask that you find the largest volume for a right circular cone inscribed in a sphere of radius 3. The book provides an image I would like some tips on where exactly I must start as I thought I had to solve for x then get y in terms of the radius r and then input that into my volume equation for the right circular cone then take the first derivative and solve for r to get the optimal value of r for the volume.

Eulers_Disciple, Sep 6, 2023
2. ### e.jane.aran

Joined:
Aug 13, 2023
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* the formula for the volume of a sphere
* the formula for the volume of a cone

From the picture:

* the radius of the base of the cone
* the expression for the height of the cone
* the radius of the sphere
* the Pythagorean Theorem

Use the Pythagorean Theorem to express y in terms of x. See where that leads....

e.jane.aran, Sep 6, 2023
Ian and sologuitar like this.