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)

Similar Questions

1. 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 d. …
2. 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.
3. 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?
4. 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 d?
5. 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.
6. Math

The following table represents the diameter of the cross section of a wire at continuous heights (feet) above the ground. Assume that each cross section is circular. Height(ft) 2 6 10 14 18 22 26 30 Diameter 2 2 2.0 1.8 1.6 1.5 1.3 …
7. 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 be …
8. 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 …
9. 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.
10. 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 decimal …

More Similar Questions