Question

How long will it take to fill a sphere-shaped vat with radius 27.7 ft with a certain liquid (d=2.13 g/mL) if it is spilling out of the hose at 12005.3 g/s?
(1.00 in = 2.54E0 cm)

Answer 1

Solution:

Radius in meters:

$R=27.7 ft=8.44 m$

Volume of the vat:

$V=4/3 (\pi R^3)=4/3 (3.14×(8.44m)^3)=2518 m^3=2.518×10^6 L$

Mass of fluid:

$m=V×\rho=2.518×10^6 L×2130 g/L=5.363×10^9 g$

Estimated time:

$t=m/Q=5.363×10^9g /12005.3g/s=44.673×10^4 s≈5.17 days$