# Algebra - Volume

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1) An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of each side of the square to be cut out.

a) Find the function V that represents the volume of the box in terms of x.

Answer:

b) Graph this function and show the graph over the valid range of the variable x..

Show Graph here.

c) Using the graph, what is the value of x that will produce the maximum volume?

Answer.

2) The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters.

a) Write h as a function of r. Keep "" in the function's equation.

Answer:

Show work in this space.

b) What is the measurement of the height if the radius of the cylinder is 3 centimeters? Round your answer to the hundredth's place.

Answer:

Show work in this space.

c) Graph this function.

Show graph here.

3) Logarithms:

a) Using a calculator, find log 1000 where log means log to the base of 10.

Answer:

b) Most calculators have 2 different logs on them: log, which is base 10, and ln, which is base e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to the computer, 0 and 1. When a computer scientist needs a logarithm, he needs a log to base 2 which is not on any calculator. To find the log of a number to any base, we can use a conversion formula as shown here:

Using this formula, find . Round your answer to the hundredth's place.

Answer:

Show work in this space.

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