Question 575067
For a square base pyramid
s=length of base side (in meters)
h=height (in meters
V=volume (in cubic meters
{{{V=(1/3)s^2*h}}}
The inverted pyramid tank has A volume of
{{{V=(1/3)3^2*8=(1/3)*9*8=24}}} cubic meters
a. The initial volume of water in the tank is the volume of a similar pyramid with
a height of 5 meters. Since the this pyramid and the 8 meter high pyramid are similar, with a height ratio of
{{{5/8}}}, the ratio of their volumes is {{{(5/8)^3}}}
So the initial volume of water in the tank is
{{{(5/8)^3*24=75/64=5.859375}}} cubic meters
b.Since the tank's volume was 24 cubic meters, the amount of water that must be added to fill the tank (in cubic meters) is
{{{24-75/64=24-5.859375=18.140625}}}
One cubic meter is 1000 liters and one US gallon is approximately 3.79L, so we approximate and convert
{{{(18.14m^3)(1000L/m^3)(1gallon/3.79L)}}}=approximately 4786 gallons
At 20 gallons per minute, with 60 minutes per hour, the hours needed to fill the tank are
{{{(4786gallons)(1minute/20gallons)(1hour/60minutes)}}}= approximately 3.99hours, so we'll say that thew answer is 4 hours.