Alg2H
10-6 More Higher Degree Functions as Math Models
VRectangular Prism = BH = lwh
Vcylinder= BH = πr2h
Vsphere= (4/3) πr3
WK I, p. 2 of 3
Vcone = (1/3) πr2h
1. An open box is to be constructed by cutting squares of length x from the corners of a piece of cardboard that
is 20 in. by 40 in. (Note: x becomes the height of the box)
a.Find the dimensions of the box that will have a volume of 1500 cubic inches. (There are 2 sets of possible answers.)
Identify the variables:
40in.
x
20in.
b. Does the box have a MAXIMUM Volume? If so, use your calculator to determine what it is.
WK I, p. 3 of 3
2. A grain silo consists of a cylindrical main section and a hemispherical roof. The cylindrical part is 30 ft tall.
a. If the total volume of the silo(including the part inside the roof section) is 15,000 cubic ft, what is the radius
of the silo, correct to the nearest tenth of a foot?
30m
b. Find the radius of the silo that will have the MAXIMUM Volume. Determine that maximum volume.