## Friday, December 14, 2012

### Textbook: Chapter 1.3 - Question #13

13) A mug for hot beverages is to be designed to keep its contents warm as long as possible.
The rate at which the beverage cools depends on the surface area of the container.
The larger the surface area of the mug, the quicker the liquid inside it will cool.

a) What is the Surface Area?
Assume that neither has a lid.

b) Which is the better mug for keeping drinks warm? Justify your answer.

SOLUTION:

To find the Surface Area of both mugs, we need to know what formula to use.
Since these look like CYLINDERS, we must use the formula for a cylinder.

Surface Area of a Cylinder = 2 π r² + 2 π r h

BUT.. there's a catch! In the question, they said assume that there is no lid.
SO.. since there are usually 2 circles in a cylinder, we must remove the area of 1 circle in the formula.
Our formula will change into:  π r² + 2 π r h

Here are my solutions: PART A

Blue Mug = 286.52 cm²
Red Mug = 298.64 cm²

PART B

The mug best for keeping drinks warm is the BLUE mug because in the question itself it stated "The larger the surface area of the mug, the quicker the liquid inside it will cool." The surface area of the blue mug is only 286.52 cm ² compared to the red mug that is 298.64 cm ²