Post a New Question

Calculus

posted by .

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 be cut from a cylindrical log of diameter d= 3 ft

  • Calculus -

    Strength, S = xy²
    But we know that
    x²+y²≤(3/2)²
    therefore, substitute
    S(x)=x((3/2)²-x²)
    For maximum strength,
    dS(x)/dx = 9/4-3*x^2 =0
    =>
    x²=3/4
    x=sqrt(3/4)
    y^2=(3/2)^2-x^2=9/4-3/4=6/4
    y=sqrt(1.5)

Answer This Question

First Name
School Subject
Your Answer

Related Questions

More Related Questions

Post a New Question