Homework Problems

1	How many cubic inches are there in a cubic foot? The answer is not 12.	√
2	Assume a dog's brain is twice is great in diameter as a cat's, but each animal's brain cells are the same size and their brains are the same shape. In addition to being a far better companion and much nicer to come home to, how many times more brain cells does a dog have than a cat? The answer is not 2.
3	The population density of Los Angeles is about 4000 people/km2. That of San Francisco is about 6000 people/km2. How many times farther away is the average person's nearest neighbor in LA than in San Francisco? The answer is not 1.5.	√
4	A hunting dog's nose has about 10 square inches of active surface. How is this possible, since the dog's nose is only about 1 in × 1 in × 1 in 1 in3? After all, 10 is greater than 1, so how can it fit?
5	Estimate the number of blades of grass on a football field.
6	In a computer memory chip, each bit of information (a 0 or a 1) is stored in a single tiny circuit etched onto the surface of a silicon chip. The circuits cover the surface of the chip like lots in a housing development. A typical chip stores 64 Mb (megabytes) of data, where a byte is 8 bits. Estimate (a) the area of each circuit, and (b) its linear size.
7	Suppose someone built a gigantic apartment building, measuring 10 km × 10 km at the base. Estimate how tall the building would have to be to have space in it for the entire world's population to live.
8	A hamburger chain advertises that it has sold 10 billion Bongo Burgers. Estimate the total mass of feed required to raise the cows used to make the burgers.
9	Estimate the volume of a human body, in cm3.
10	How many cm2 is 1 mm2?	Solution, p. 275
11	Compare the light-gathering powers of a 3-cm-diameter telescope and a 30-cm telescope.	Solution, p. 275
12	One step on the Richter scale corresponds to a factor of 100 in terms of the energy absorbed by something on the surface of the Earth, e.g., a house. For instance, a 9.3-magnitude quake would release 100 times more energy than an 8.3. The energy spreads out from the epicenter as a wave, and for the sake of this problem we'll assume we're dealing with seismic waves that spread out in three dimensions, so that we can visualize them as hemispheres spreading out under the surface of the earth. If a certain 7.6-magnitude earthquake and a certain 5.6-magnitude earthquake produce the same amount of vibration where I live, compare the distances from my house to the two epicenters.	Solution, p. 275
13	In Europe, a piece of paper of the standard size, called A4, is a little narrower and taller than its American counterpart. The ratio of the height to the width is the square root of 2, and this has some useful properties. For instance, if you cut an A4 sheet from left to right, you get two smaller sheets that have the same proportions. You can even buy sheets of this smaller size, and they're called A5. There is a whole series of sizes related in this way, all with the same proportions. (a) Compare an A5 sheet to an A4 in terms of area and linear size. (b) The series of paper sizes starts from an A0 sheet, which has an area of one square meter. Suppose we had a series of boxes defined in a similar way: the B0 box has a volume of one cubic meter, two B1 boxes fit exactly inside an B0 box, and so on. What would be the dimensions of a B0 box?	√
14	Albert Einstein, and his moustache. Estimate the mass of one of the hairs in Albert Einstein's moustache, in units of kg.
15	According to folklore, every time you take a breath, you are inhaling some of the air molecules exhaled in Caesar's last words. Is this true? If so, how many molecules?
16	The Earth's surface is about 70% water. Mars's diameter is about half the Earth's, but it has no surface water. Compare the land areas of the two planets.
17	The traditional Martini glass is shaped like a cone with the point at the bottom. Suppose you make a Martini by pouring vermouth into the glass to a depth of 3 cm, and then adding gin to bring the depth to 6 cm. What are the proportions of gin and vermouth?	Solution, p. 275
18	The central portion of a CD is taken up by the hole and some surrounding clear plastic, and this area is unavailable for storing data. The radius of the central circle is about 35% of the radius of the data-storing area. What percentage of the CD's area is therefore lost?	√
19	The one-liter cube in the photo has been marked off into smaller cubes, with linear dimensions one tenth those of the big one. What is the volume of each of the small cubes?	Solution, p. 275
20	A cute formula from trigonometry lets you find any angle of a triangle if you know the lengths of its sides. Using the notation shown in the figure, and letting s = (a + b + c)/2 be half the perimeter, we have Show that the units of this equation make sense.	Solution, p. 275
21	Estimate the number of man-hours required for building the Great Wall of China.	Solution, p. 275