Please show work. 2.A box with an open top has vertical sides, a square bottom,
ID: 2833827 • Letter: P
Question
Please show work.
2.A box with an open top has vertical sides, a square bottom, and a volume of 256 cubic meters. If the box has the least possible surface area, find its dimensions.
Height = (include units)
Length of base = (include units)
3.A fence 6 feet tall runs parallel to a tall building at a distance of 6 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
4.If 1100 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
Volume = __cubic centimeters.
5.A rancher wants to fence in an area of 2500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
6.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 possibe Norman window with a perimeter of 20 feet?
Width = Height =
Explanation / Answer
3.)
Let:
A = the angle the ladder makes with the ground
L = length of the ladder
L = 6/sinA + 5/cosA
dL/dA = -6cos/sin^2A + 5sinA/cos^2A = 0
-6cos^3A + 5sin^3A = 0
sinA/cosA = tanA = (6/5)^(1/3) = 1.06266
A = 46.73997 degrees
6/sinA = 8.23892
5/cos A = 7.29596
L = 8.23892 + 7.29596 = 15.53488 FT