Functions from formulas

1
Functions from formulas

• Find the area of a circle as a function of
• A) radius
• B) diameter
• C) circumference

2
Functions from formulas

• Suppose that the surface area of a closed right
  circular cylinder is 30p sq cm. Express the
  volume of the cylinder as a function of its
  radius r.

3
Maximum problem

• A square of side x inches is cut out of each
  corner of an 8 x 15 in. piece of cardboard and
  the sides are folded up to form an open-topped
  box. How big should the cut-out squares be in
  order to produce the box of maximum volume?

4
Mixture problem

• How much 10 solution and how much 45 solution
  should be mixed together to make 100 gallons of
  25 solution?

5
Antenna

• A small satellite dish is packaged with a
  cardboard cylinder for protection. The parabolic
  dish is 24 in. in diameter and 6 in. deep, and
  the diameter of the cardboard cylinder is 12 in.
  How tall must the cylinder be to fit in the
  middle of the dish and be flush with the top of
  the dish?

6
Sphere

• Express the volume of a sphere in four different
  ways as a function of
• A) the radius
• B) the diameter
• C) the circumference of an equator-type circle
• D) the area of an equator-type circle

7
Functions from formulas

• An oil tank is in the shape of a right circular
  cone with a height of 15 feet and a radius of 4
  feet. Suppose the tank is filled to a depth of h
  feet. Let x be the radius of the circle on the
  surface of the oil. Express the volume of oil in
  the tank as a function of x.

8
Functions from verbal description

• Grain is leaking through a hole in a storage bin
  at a constant rate of 8 cubic inches per minute.
  The grain forms a cone-shaped pile on the ground
  below. As it grows, the height of the cone always
  remains equal to its radius. If the cone is one
  foot tall now, how tall will it be in one hour?