F. (11) (2 puntos posibles)

Question

Consider a circular cone with base of radius a and a height of a.

Find the vertical cylinder of largest volume inside this cone.

In terms of a, what is the radius of this largest cylinder?

(Enter ∗ for multiplication: type 2*x for 2x. Enter / for division: type 1/2 for 12. Enter ∧ for exponentiation: type e∧x for ex. Type sqrt(2) for 2√.)

radius:
sin responder
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In terms of a, what is the height of this largest cylinder?

(Enter ∗ for multiplication: type 2*x for 2x. Enter / for division: type 1/2 for 12. Enter ∧ for exponentiation: type e∧x for ex. Type sqrt(2) for 2√.)

height:
sin responder