Expert: Sherry Wallin - 2/27/2009

Question
1. Many of the amenities at a local ski hill are run using gas generators.
To transport gasoline to the top of the mountain, a special trailer has
been designed. The trailer bed is in the shape of a square with a side
length of 1.5 m. they wish to attach a cylindrical shaped gas tank to the
trailer which is as large as possible, but cannot be taller than the
trailer bed is. Determine the dimensions, volume and surface area of the
gas tank.


2. When shipping ice cream, melting is understandably a big concern..A
standard container of ice cream contains 1 L, or 1000 cm(to the power of 3)
of ice cream.
a. What would be the optimal dimensions (radius and height) to minimize
surface area be? b. What would the surface area be?

3. The Goodsmell perfume producing company has a new line of perfume and is
designing a new bottle for it. Because of the expense of the glass required
to make the bottle, the surface area must be less that 150 cm(squared). the
company also wants the bottle to hold at least 100 mL of perfume. The
design under consideration is in the shape of a cylinder. a. Determine the
maximum volume possible for a cylindrical bottle that has a total surface
area of less than 150 cm(squared).
b. Report the dimensions of the bottle and the corresponding surface area
and volume. c. This cylindrical perfume bottle needs to be boxed in a prism
for sale on store shelves. The perfume company would like a box with the
smallest possible surface area which will hold your design for the perfume
bottle. Find the dimensions of the box and calculate its surface area.


4. ED is a midsegment of triangle ABC. CD = 3.5 cm and BE =
3 cm  <BAC = 75 degrees   <ACB = 30 degrees

What is the length of AD? What is the length of AB? Find the measure of <ADE?   Find the measure of <AED?  

5. A parallelogram is a rectangle. Prove or deny this statement. Justify
your answer. Diagrams will enhance your explanation.

Thank you.  

Answer
Hmmm...which one would you like to see worked and explained? The purpose of this site is to help you learn so you need to focus on one problem and ask for assistance. It is also helpful if you explain what you understand and what you don't understand.

I'll talk you through 5

First, a parallelogram could be a rectangle but it is not the case that all parallelograms are rectangles. One way to show something is not true is to find a counter example, an example where it isn't true all the time. A rhombus is a parallelogram that is NOT a rectangle. The primary reason a rhombus is not a rectangle is that a rhombus has angles that are not equal 90 degrees. It is a parallelogram because it has two pairs of opposite sides that are parallel.