4. An important question to consider when thinking about global warming is, "If the ice sheets near the poles melt, how much will the sea level rise?" This seems like a difficult question, given the odd shapes of both the ice sheets and the oceans. But there are some accurate approximations that allow the answer to be estimated fairly accurately with reasonably simple calculations. The crucial idea is that both the thickness of the ice sheets and the amount of sea level rise are extremely small compared to the radius of the Earth. The radius of the Earth is about 6 x 106 m-more than 6000 miles; by comparison, the ice sheet thicknesses we'll be concerned with are single-digit miles, and the sea level rises will be in dozens of feet. As a result, we can essentially ignore the curvature of the Earth when answering this question. We can imagine peeling the map of the earth off a globe and flattening it out (by making cuts, not by stretching it, so that we preserve the area). Then, both the ice and the sea level rise can be treated as right (not tilted) cylinders (though with funny-shaped bases and tops). Since we know that the volume of a right cylinder is the area of the base times the height, we can easily estimate all the volumes we need. The error in these approximations is on the order of the height of the cylinder considered divided by the radius of the earth: a very small number. The picture below shows a schematic representation of this. (The height of the ice mass-the small cylinder-is greatly exaggerated in the picture; if it were drawn to scale, you wouldn't be able to see it at all.) a) Suppose we've flattened the surface of the Earth in our imaginations, as illustrated on the right hand side of the picture. Assume that the ice sheet to be considered covers an area A and has thickness d. Note that the oceans cover about 75% of the Earth's surface, and that the surface area of a sphere is 472, where r is the radius of the sphere. Come up with an equation that will allow you to calculate h, the rise in sea level due to the melting of the ice sheet, in terms of A, d, and r (r being the radius of the Earth). As always, explain your reasoning.

4. An important question to consider when thinking about global warming is, "If the ice sheets near the poles melt, how much will the sea level rise?" This seems like a difficult question, given the odd shapes of both the ice sheets and the oceans. But there are some accurate approximations that allow the answer to be estimated fairly accurately with reasonably simple calculations. The crucial idea is that both the thickness of the ice sheets and the amount of sea level rise are extremely small compared to the radius of the Earth. The radius of the Earth is about 6 x 106 m-more than 6000 miles; by comparison, the ice sheet thicknesses we'll be concerned with are single-digit miles, and the sea level rises will be in dozens of feet. As a result, we can essentially ignore the curvature of the Earth when answering this question. We can imagine peeling the map of the earth off a globe and flattening it out (by making cuts, not by stretching it, so that we preserve the area). Then, both the ice and the sea level rise can be treated as right (not tilted) cylinders (though with funny-shaped bases and tops). Since we know that the volume of a right cylinder is the area of the base times the height, we can easily estimate all the volumes we need. The error in these approximations is on the order of the height of the cylinder considered divided by the radius of the earth: a very small number. The picture below shows a schematic representation of this. (The height of the ice mass-the small cylinder-is greatly exaggerated in the picture; if it were drawn to scale, you wouldn't be able to see it at all.) a) Suppose we've flattened the surface of the Earth in our imaginations, as illustrated on the right hand side of the picture. Assume that the ice sheet to be considered covers an area A and has thickness d. Note that the oceans cover about 75% of the Earth's surface, and that the surface area of a sphere is 472, where r is the radius of the sphere. Come up with an equation that will allow you to calculate h, the rise in sea level due to the melting of the ice sheet, in terms of A, d, and r (r being the radius of the Earth). As always, explain your reasoning.