Show all work. Draw diagrams and explain answers as needed.

Question 1: A large storage tank holds 2900 m³ of a liquid mixture that has 112% of the density of water. The tank is in an empty warehouse with 40,000 ft² of empty floor space. If over a weekend the tank leaks and empties on to the floor: .

a) How deep is the liquid on Monday morning?

b) The liquid gets pumped out and carried away by trucks that can carry 9000 kg of liquid each. How many truck loads are required?

Question 2: The large sheet of ice diagrammed below has uniform thickness h=28.5 m and a mass of 2.25 x 10⁸ kg. Its identical upper and lower surfaces each have area A and are flat with irregular outlines.

a) Determine the area A. (Look up the density of ice.)

b) If the same ice sheet were in the shape of a cube, what would be the length of each side of the cube?

Question 3: The Earth is approximately spherical in shape with a radius of 6.4 x 10⁶ m. Approximately 70% of the surface area of Earth is ocean and the average depth of Earth's oceans is 1 mile (order of magnitude).

a) Use the above information to determine the total volume of seawater on the Earth1 in cubic meters. Determine the mass of seawater on Earth based on your volume calculation.

b) Determine the volume of the Earth. What fraction of the Earth is seawater, by volume? What fraction of the Earth is seawater, by mass? Why do these fractions differ?

c) Recall the activity we performed in class using eyedroppers. Use a round number estimate of the number of drops per milliliter to estimate the number of drops of water in the oceans.

The volume of a spherical shell of thickness h covering the surface of a sphere of radius R is given approximately by 4πR2 h. The approximation is very accurate as long as h << R.

Question 4: Imagine a cylindrically shaped object with diameter D and height (length) h.

a) h/D = 0.7 for the given values. Someone makes a scale model of the object that is either larger or smaller than the actual cylinder. If the scale model is to look like the actual cylinder how must the quantities h and D be related for the scale model? Explain your reasoning2 .

b) Describe how h and D would have to be related if the cylinder changed size and the rescaled cylinder was distorted so that it was narrower and stretched vertically compared to the original? Repeat for a rescaled cylinder that was distorted so that it was wider and squished vertically. Explain your reasoning in each case. Don't make up values for D and h. There are an infinite number of possibilities in each case, but these questions have definite answers.

c) Sketch on the same set of axes (no need for graph paper) three linear functions: one describing how h is related to D for rescaled cylinders that are not distorted, a second describing the stretched vertically cylinders, and a third describing the squished cylinders. Describe the slope and intercept of each line.