Calculus

posted by .

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 47 feet?

  • Calculus -

    p = W + 2L + πW/2 = 47
    2L = 47 - W - πW/2
    L = 23.5 - 1.28W

    A = WL + π(W/2)^2/2
    = W(23.5 - 1.28W) + .327W^2
    = 23.5W - 1.28W^2 + .327W^2
    = 23.5W - .953W^2

    max area at W = 23.5/1.906 = 12.3 ft
    L = 7.756

    perimeter = 12.3 + 2*7.756 + 1.57*12.3 = 47.1 (close enough)

    area = 12.3*7.756 + 3.14*6.15 = 114.7 ft^2

  • Calculus -

    it says incorrect

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 33 feet?
  2. Math (:

    My answer doesn't make sense. It's too big. A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman …
  3. Calculus

    A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 22 feet?
  4. Calculus

    A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 40 feet?
  5. Calculus

    A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 30 feet?
  6. Calculus

    A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 33 feet?
  7. Calculus

    A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 49 feet?
  8. calculus

    A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 31 feet
  9. Calculus

    A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 31 feet?
  10. Calculus - Optimization

    A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 38 feet?

More Similar Questions