1. A child loves to watch as you refill a transparent plastic bottle with shampoo. Every horizontal cross-section is a circle, but the diameters of the circles have different values, because the bottle is much wider in some places than in others. You pour in bright green shampoo with constant volume flow rate 15.0 cm3/s.
(a) At what rate is the level of the shampoo in the bottle rising at a point where the diameter of the bottle is 6.10 cm?
(b) At what rate is the level of the shampoo rising at a point where the diameter is 1.35 cm?
2. Assume there are 140 million passenger cars in the United States and the average fuel consumption is 20 mi/gal of gasoline. If the average distance traveled by each car is 11000 mi/yr, how much gasoline would be saved per year if average fuel consumption could be increased to 25 mi/gal?
3. The distance from the Sun to the nearest star is about 4 multiplied by 1016 m. The Milky Way galaxy is roughly a disk of diameter ~ 1021 m and thickness ~ 1019 m. Find the order of magnitude of the number of stars in the Milky Way. Assume the distance between the Sun and our nearest neighbor is typical.



Thank you so much...