1Small spheres of equal mass are made of lead (density 11.3 g/cm^3), silver (10.5 g/cm^3), and aluminum (2.70 g/cm^3)Which sphere has the largest diameter, and which has the smallest?2Recently, one of the text authors completed an exactly 10-mi road race, in a time of 1 hour, 25 min, and 14 s(a) What was the runner's average speed in miles per hour? (b) What was the runner's pace in minutes and seconds per mile?3The U.Squarter has a mass of 5.67 g and is approximately 1.55 mm thick.(a) How many quarters would have to be stacked to reach 575 ft, the height of the Washington Monument? (b) How much would this stack weigh? (c) How much money would this stack contain? (d) In 2004 the national debt was $7.2 trillionHow many stacks like the one described would be necessary to pay off this debt?
1lead (density 11.3 g/cm^3), silver (10.5 g/cm^3), and aluminum (2.70 g/cm^3) given that all three spheres have the exact same mass (m), then the volume for each is: lead volume m / 11.3 0.0885m silver volume m / 10.5 0.0952m aluminum volume m / 2.7 0.3704m Diameter of a sphere is directly proportional to its volumeTherefore, since lead has the largest volume, then it has the largest diameterAnd since aluminum has the smallest volume, then it has the smallest diameter 260 minutes 60 seconds 1 hour 1 hour x - x - 3600 seconds 1 hour 1 minute 60 seconds 25 minutes 25 minutes x - 1500 seconds 1 minute Therefore, 1 hour + 25 minutes + 14 seconds 3600 + 1500 + 14 5114 seconds Since the runner completed the 10 mile race in 5114 seconds, then 10 miles 60 seconds 60 minutes 36000 - x - x - - 7.04 mph 5114 seconds 1 minute 1 hour 5114 3mass 5.67 g thickness 1.55 mm 2.54 cm 12 inches 10 mm 575 feet 575 feet x - x - x - 175,260 mm 1 inch 1 foot 1 cm So 175,260 mm - 113,070.97 quarters rounded up to 113,071 quarters 1.55 mm A stack of 113,071 quarters would weigh 5.67 grams 113,071 quarters x - 641,112.57 grams 1 quarter I think you have enough information above to work out the national debt on your own.
