Calculus

A rectangular beam is cut from a cylindrical log of radius 30 cm. The strength of a beam of width w and height h is proportional to wh^2. Find the width and height of the beam of maximum strength.

Is the width 45 and the height 20.

  1. 👍 0
  2. 👎 0
  3. 👁 232
asked by George
  1. Hey, the height is surely more than the width for strength
    w = 1/2 width
    h = 1/2 height
    15 = sqrt(w^2+h^2)
    w^2+h^2 = 225
    so
    h^2 = 225 - w^2
    then
    strength = s = k w h^2 = k w(225-w^2)
    find where ds/dw = 0
    s = k (225 w - w^3)
    ds/dw = k (225 - 3 w^2) =0
    w^2 = 225/3 = 75
    then h^2 = 225 -75 = 150
    so
    w = 5 sqt3 and width = 10 sqrt 3
    h = 5 sqrt 6 and length = 10 sqrt 6
    by the way
    h/w = sqrt 2 = 1.41

    1. 👍 0
    2. 👎 0
    posted by Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    A rectangular beam is cut from a cylindrical log of radius 25 cm. The strength of a beam of width w and height h is proportional to wh2. (See Figure 4.70.) Find the width and height of the beam of maximum strength.

    asked by Maria on November 1, 2011
  2. math

    A rectangular beam is cut from a cylindrical log of radius 15 cm. The strength of a beam of width w and height h is proportional to wh^2. Find the width and height of the beam of maximum strength. (Round your answers to two

    asked by Leila on October 29, 2015
  3. Calculus

    The strength of a beam with rectangular corss-section is directly proportional to the product of the width and the square of the depth (thickness from the top to bottom of the beam). Find the shape of the strongest beam that can

    asked by Liz on May 5, 2012
  4. Calculus

    The strength of a beam with rectangular corss-section is directly proportional to the product of the width and the square of the depth (thickness from the top to bottom of the beam). Find the shape of the strongest beam that can

    asked by Candy on March 10, 2012
  5. Calculus1

    The strength, S, of a rectangular wooden beam is proportional to its width times the square of its depth. Find the dimensions of the strongest beam that can be cut from a 12 inch diameter cylindrical log.

    asked by ACDub on April 3, 2014
  6. calculus

    The strength of a rectangular beam is proportional to width*depth^2. What are the dimensions of the strongest rectangular beam that can be cut out of a 12 inch diameter log?

    asked by Susan on December 4, 2010
  7. calculus

    Hi, I'm having trouble with this problem... "If the strength of a rectangular beam of wood varies as its breadth and the square of its depth, find the dimensions of the strongest beam that can be cut out of a round log, diameter

    asked by Creating a formula from 2 variables on January 29, 2008
  8. math

    The stiffness of a given length of beam is proportional to the product of the width and the cube of the depth. Find the shape of the stiffest beam which can be cut from a cylindrical log (of the given length) with cross-sectional

    asked by manjeet on April 7, 2018
  9. Calculus

    I need help with this question: The strength of a beam with a rectangular cross section varies directly as x and as the square of y. What are the dimensions of the strongest beam that can be sawed out of a round log with diameter

    asked by John on February 25, 2011
  10. math

    The stiffness S of a rectangular beam is proportional to its width (w) times the cube of its depth/height (h). find the dimensions (i.e.: w and h) of stiffest beam that can be cut from a log which has a circular cross-section with

    asked by deel on August 9, 2012

More Similar Questions