Question

If you had Avogadro's Number of water drops, it would fill a swimming pool with a 1 mile diameter and with a depth of what?

Answer 1

9198000 miles deep

Step-by-step explanation:

Assuming a circular swimming pool, we can calculate the volume of the swimming pool to be 0.25 * pi * depth mi^3 (radius is 0.5 miles).
Every drop of water contains about 0.05 mls, and if you had 6.022*10^23 drops, you would have 0.05 * 6.022*10^23 = 3.011*10^22 mls of water.
Using the conversion factor 4.16818183*10^15 ml = 1 mi^3, we calculate that there are 7224090 mi^3 of water. Because volume = 7.2241*10^6 = 0.25 * pi * depth, depth = 7.2241*10^6 / (0.25*pi) = 9198000 miles deep.

Answer 2

The depth of a swimming pool with a 1 mile diameter when filled with Avogadro's number of water drops cannot be calculated without the specific volume of a water drop, but it would be extremely deep.

Step-by-step explanation:

The student is essentially asking how deep a swimming pool of a 1 mile diameter would be if it were filled with Avogadro's number of water drops. To answer this, we need to recall what Avogadro's number is and relate it to the volume of water in each drop, then determine the volume of the pool.

Avogadro's number, which is approximately 6.022 x 1023, represents the number of particles, such as atoms or molecules, in one mole of a substance. Based on the provided information, a single drop of water contains about 1022 molecules of water. However, what we require is the volume that these molecules would occupy, not the number of molecules itself.

The volume of Avogadro's number of water drops would be immense, far more than enough to fill a swimming pool. Therefore, without the exact volume of 'a water drop' and a precise calculation, we cannot give an accurate depth. Nonetheless, we can affirm that the depth would be extraordinarily deep, likely many kilometers, due to the vast number of molecules represented by Avogadro's number.