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# Units conversion, volume density and other physical quantities.

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A corner construction lot has the shape of a right triangle. If the two sides perpendicular to each other are 37 m long and 42.3 m long, respectively, what is the length of the hypotenuse?

75. The lightest solid material is silica aerogel, which has a typical density of only about
3
0.10 g/cm . The molecular structure of silica aerogel is typically 95% empty space.
3
What is the mass of one 1m of silica aerogel?

79. A light-year is a unit of distance corresponding to the distance light travels in a vacuum in 1 year.
8
If the speed of light is 3.00 x 10 m/s, what is the length of a light-year in meters?

85. The Channel Tunnel, or "Channel" which runs under the English Channel between Great Britain and France, is 31 mi long. (There are actually three separate tunnels.) A shuttle train that carries passengers through the tunnel travels with an average speed of 75 mi/h. On average, how long, in minutes, does it take the shuttle to make a one-way trip through the Chunnel?

87. A student wants to determine the distance of a small island from the lakeshore. He first draws a 50-m line parallel to the shore. Then, he goes to the ends of the line and measures the angles of the lines of sight from the island relative to the line he has drawn. The angles are 30 degrees and 40 degrees. How far is the island from the shore?

89. Suppose you are paying \$1.20 for 1 gal of gas. Then the United States switches to SI units, and you find that gas costs \$0.32/L. Which is the greater cost for gas?

93. A rectangular block has the dimensions 2.8 cm, 9.5 cm, and 8.7 cm. Estimate the volume of the block in cubic centimeters.

95. A cylindrical drinking glass has an inside diameter of 8.0 cm and a depth of 12 cm. If a person drinks a completely full glass of water, how much water (in liters) will be consumed?

99. A car is driven 13 miles east and then a certain distance due north and ends up at a position of 25 degrees north of east.

a) The distance traveled by the car due north is 1) less than, 2) equal to, or 3) greater than 13 miles. Why?
b) What distance does the car go due north?

101. A hollow spherical ball of radius 12 cm is filled with water. What is the mass of water inside the sphere, in kilograms?