Estimate the number of raindrops needed to fill a volume of 1m $\times$ 1m $\times$ 1cm. A)10³ B)10⁵ C)10⁷ D)10⁹ E)10¹¹

Question

Quizplus · Accepted Answer

Volume of 1 cm = 0.000001 m^3
Volume of a raindrop (assumed spherical) = (4/3) * π * r^3, where r is approximately 0.002 m (2 mm)
Using these values, we can estimate the number of raindrops needed to fill the volume of 1 cm:
(0.000001 m^3) / [(4/3) * π * (0.002 m)^3] = 655.13
Rounding up, we get approximately 656 raindrops.
The only answer choice that comes close to this is C, which has 10^17 raindrops (i.e. 10 followed by 17 zeroes). This is a reasonable estimate, considering that 1 m x 1 m x 1 cm is a relatively small volume compared to the vast expanse of the atmosphere from which rain falls.

Estimate the Number of Raindrops Needed to Fill a Volume ×\times×

Estimate the Number of Raindrops Needed to Fill a Volume $\times$