- With a pencil and paper:
- Draw a large square
- Insrcribe a circle inside the large square
- Inscribe a small square inside the circle
- What is the ratio of the area of the large square to the area of the small square?
Assume the width of the large square is d. The diameter of the circle inside the square is d and its radius is r = d/2.
The small circle’s diagonal measures 2r. Therefore its area is 2r2. The large square’s area is d2 or 4r2.
Therefore the ratio of the areas is 2:1.
- You wake up one morning to find an intact Boeing 747 in your front yard. You need to rent a crane to remove it. You need to determine the weight of the airplane in order to rent the correct crane. How do you figure out the weight of the airplane?
I’d look it up on Google.
But assuming I don’t have Google I’d guess like this:
Plane can carry 500 passengers. Each passenger weighs 200 lbs plus about 100 lbs for a chair and 100 lbs for luggage and food. Let’s round up to 1000 lbs. That comes out to 500,000 lbs.
Let’s assume the plane should be about 10 times heavier to carry such a load which is about the ratio between a car and a full passenger load.
Therefore I will guess a Boeing 747 weighs between 5 and 10 million lbs.
- On a traditional analog clock, how many degrees separate the hour and minute hands at 3:15?
Minute hand is at 90 degrees, where 3 is located.
The hour hand is at the 3 plus 25% of the way to 4. There is 360/12 degrees between each numeral.
Therefore the difference between the hour and minute 360/12/4 which is 7.5 degrees.