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

Textbook- Chapter 2.4, Page 79, Question # 15

Kai needs to replace the strip of laminate that is glued to the vertical faces on a square tabletop.
The tabletop has an area of 1.69 m². What length of laminate does she need?

SOLUTION:

Area of a square = Side x Side (length x width)

A = 1.69 m²


Length = √area of square

L = √1.69 m²

L = 1.3 m   


Verify:  1.3² = 1.3 m x 1.3m
                     =  1.69 m²



SSA:  The length Kai needs for the laminate is 1.3 m long.

TEXTBOOK: Pg. 61, Question # 21

Andrew drove his car 234 km from Dawson to Mayo in Yukon Territory in 3 h. Brian drove his truck along the same route at an average speed of 5 km/h greater than Andrew's average speed. How much less time did Brian take, to the nearest minute.


SOLUTION:  

Andrew: 234 km in 3 hours    Average Speed = ?

                        FORMULA:   Speed = Distance
                                                                               Time
                                                                     

                                                                       78 = 234  
                                                                                  3
                                                   
                                                                  Speed = 78 km/ h

Brian: Has Average Speed of 5 km/ h greater than Andrew's.

                                           78 + 5 = 83 
                       Brian's Average Speed is 83 km/ h 

To find out how much LESS time Brian took, we need to find out how much time Brian took FIRST!

To find how much time Brian took, you have to use the FORMULA: Distance divided by Speed to get the TIME.

                                        D = T
                                        S
       
                                     234 km  ≈ 2.819
                                    83 km/ h   

                          Time ≈ 2.819 hours 

     
2.819 hours x 60 ≈ 169 minutes

169 minutes = 2 hours 49 minutes
(2 hours = 120 minutes, add remaining 49 minutes)

Time = 2 hours and 24 minutes


Now we subtract Brian's and Andrew's times to find out how much less time Brian took.

Andrew's Time - Brian's Time = Difference

3 hours 00 minutes - 2 hours 49 minutes = 11 minutes 

SSA:  It took Brian 11 minutes less than Andrew to get from Dawson to Mayo in Yukon Territory.