More importantly, we realized that we had brought a round object to a school that was about to celebrate pi, so I posed a few questions about it and promised to post some more.
EarthView has a flat bottom (so that it does not roll around like a hamster ball). That bottom is a circle 12 feet in diameter, containing the continent of Antarctica and the Southern Ocean. If not for the flat bottom, EarthView would be a sphere 22 feet in diameter. For the questions below, it is probably best to imagine it as a perfect sphere. With these two dimensions -- and some formulas that might be in the back of your math book or at 1728.com -- you can calculate answers to the following. Be sure to keep track of your measurement units!
- What is the circumference of the flat, bottom part of EarthView?
- What is the area of the flat, bottom part of EarthView?
- If 24 people are in EarthView, how much space does each person have to stand?
- What is the surface area of EarthView (assuming it is a sphere) in square feet? What is the surface area in square yards?
- What is the volume of air in EarthView?
- If it takes six minutes to fill EarthView with our trusty fan, what is the rate of air flow in cubic feet per minute?
- If we filled EarthView with water, how much would it weigh? (For this you need to look up or calculate the density of water in pounds per cubic foot.)
- What is the surface area of the Mapparium?
- What is the volume of the Mapparium?
- How much bigger is the surface area of the Mapparium, compared to EarthView?
- How much greater is the volume of Mapparium than that of EarthView?
- What is the surface area of the earth in square miles? In square kilometers?
- What is the volume of the earth in cubic miles? In cubic kilometers?
- The surface area of the globe in square inches and in square feet.
- The volume of the globe in cubic inches and cubic feet.