Final answer:
To calculate how far the jar will sink, use the formula for the volume of a cylinder and divide it by the volume of water displaced. To calculate how much honey it will take for all but 0.00000075% of the jar to be below the surface of the water, find the volume of honey needed by dividing the volume of the jar by the density of honey and then multiply this volume by the density of honey to find the mass of honey.
Step-by-step explanation:
To calculate how far the jar will sink, we need to find the volume of the jar and divide it by the volume of water displaced. The volume of the jar can be calculated using the formula for the volume of a cylinder: V = π r^2 h, where r is the radius and h is the height. Plugging in the given dimensions, we get V = π (2.375 miles)^2 (1.25 miles). To find the volume of water displaced, we can use the same formula with the inside radius of the jar: V_water = π (2.375 miles - 0.0375 feet)^2 (1.25 miles). Dividing V by V_water will give us the fraction of the jar submerged, which we can multiply by the height of the jar to find how far it sinks.
Now, to calculate how much honey it will take for all but 0.00000075% of the jar to be below the surface of the water, we need to find the volume of the honey. Since the density of honey is 3.45 times that of water, the density of honey is 1.075 g/cm^3 * 3.45 = 3.70875 g/cm^3. We can use the same method as before to find the volume of honey needed, by dividing the volume of the jar by the density of honey. Multiplying this volume by the density of honey will give us the mass of honey.