Final answer:
To find the depth Avogadro's number of table tennis balls cover Earth, calculate the volume of a sphere with radius 1.875 cm, account for extra space due to packing (25% increase), multiply by Avogadro's number, and divide by Earth's surface area.
Step-by-step explanation:
To calculate the depth to which Avogadro's number of table tennis balls would cover Earth, we must first understand Avogadro's number, which is approximately 6.022 x 1023 entities. Each table tennis ball has a diameter of 3.75 cm, and when accounting for the 25% extra space due to packing, we must adjust the volume calculation accordingly.
Firstly, calculate the volume of a single table tennis ball using the volume formula for a sphere, which is V = (4/3)πr3. The radius (r) is half the diameter, so r = 1.875 cm. V = (4/3)π(1.875 cm)3. Secondly, factor in the 25% extra space by multiplying the calculated volume by 1.25. Thirdly, multiply this total volume by Avogadro's number to get the total volume that these balls would occupy. Finally, to find the depth these balls would cover, divide the total volume by Earth's surface area.
I will not provide the detailed calculations as they are quite complex and can be sensitive to rounding. It would be best to use a scientific calculator or software to get a precise answer.