Calculus: Optimization

I have no idea how to approach this problem, if someone knows just how to relate h, r with H,R, that would be extremely helpful and I can workout the rest! Thank you in advance.

Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the
center of the base of the larger cone, and its base is parallel to the base of the larger cone. If
you choose the upside-down cone to have the largest possible volume, what fraction of the
volume of the larger cone does it occupy? (Let H and R be the height and radius of the large
cone, let h and r be the height and radius of the small cone. The formula for the volume of a cone is V= 1/3pi(r^2)h

  1. 👍 0
  2. 👎 0
  3. 👁 180
asked by Jazz

    From his smaller volume V, take the derivative, set to zero, solve for r (for max volume.

    Then determine the ratio

Respond to this Question

First Name

Your Response

Similar Questions

  1. Tan^2 Integrals

    I'm having a hard time understanding how to do Integrals involving tan^2. I have two problems: 1. Find the integral of (tan^2 y +1)dy 2. Find the integral of (7tan^2 u +15)du 1. My approach to it is to replace the tan^2 y portion

    asked by Anonymous on December 10, 2013
  2. Calculus

    f(x) = [3/x^2] - [5/x^7], F(x) is the antiderivative of f(x) with F(1)=0. F(x) = ? I have no idea how to approach this problem. The fractions are scaring me.

    asked by Z32 on November 6, 2009
  3. Calculus

    limit of ((1/x) - (1/|x|) as x approaches x from the left side. i have no idea how to approach this problem.

    asked by Deb on September 15, 2009
  4. Math subject Calculus

    Hi there I am having some difficulties to solve this problem from my homework package and i don't understand how to approach this problem. Please help me by giving me advice on how to approach this problem. Let z = xsin(x/y), y

    asked by shylo on October 24, 2009
  5. calculus

    Solve for all real values of x. 3tan^2x = 3^1/2 tan x I have no idea how to approach this problem.

    asked by Tracy on January 24, 2010
  6. Physics

    r vector=(340m, 39 degrees below positive x-axis) What is rx and ry? I have no idea how to do or approach this problem, anyone please help and explain how to do this? Thank you!

    asked by Sher on September 12, 2011
  7. Math

    Let z be a complex number, and let n be a positive integer such that z^n = (z + 1)^n = 1. Prove that n is divisible by 6. I have no idea how to approach this problem!

    asked by Katie on May 6, 2016
  8. Cultural Ant.

    What is the meaning of Theoretical approach. Form my homework question my teacher asks me to explain the theoretical approach the author adopts for her investigation. However, I have no idea what a theoretical approach is :(

    asked by Renee on April 15, 2014
  9. Science

    You are a Chemical engineer, trying to synthesize N2H4(l). Your boss suggests that you try to synthesis it from the elements, nitrogen and hydrogen, at 25 celsius and 1.0 atm (since this would be a cheap way of doing it). Write a

    asked by Sue on July 26, 2012
  10. Math - vectors

    For what value of t are these two vectors parallel? a) r = 4i + tj and s = 14i - 12j What I Know: vectors are parallel if one is a scalar multiple of the other. I need to find a way that r and s relate by finding what number you

    asked by Anna on September 7, 2016

More Similar Questions