A water tower in New York City has the shape of a cylinder with a cone on top. The cylinder has a diameter of 12 feet and a height of 15 feet. The roof has an inclination angle of 25o. There are 7.48 gallons in a cubic foot. If residents of an apartment building are using the water from the tower at an average rate of 56 gallons per minute, determine how long, to the nearest minute, it will take to drain the entire tower.

number of minutes to drain the entire tower = 241 minutes (nearest minutes)

Step-by-step explanation:

The water tower has the shape of a cylinder with a cone on top. The volume of the water tower can be find when you find the sum of the volume of the cylinder and the cone.

Therefore,

volume of the cylinder = πr²h

where

r = 12/2 = 6 ft

h = 15 ft

volume = π * 6² * 15

volume = π * 36 * 15

volume of the cylinder = 540π

Volume of the cone = 1/3πr²h

r = 6 ft

Using tangential ratio we can find the height which is the opposite side of the triangle

tan 25° = opposite/adjacent

tan 25° = h/6

cross multiply

h = 6 tan 25°

h = 6 * 0.46630765815

h = 2.79784594893

h = 2.8 ft

volume of the cone = 1/3πr²h

volume = 1/3 * π * 36 * 2.8

volume = 100.8π/3

volume = 33.6π

Volume of the tower system = 540π + 33.6π = 573.6π

volume of the tower system = 573.6 * 3.14 = 1801.104 ft³

1 cubic ft = 7.48 gallons

1801.104 cubic fit = ? gallons

cross multiply

gallons = 1801.104 * 7.48

gallons = 13472.25792 gallons

The residents drains the water at the rate of 56 gallons per minute. Therefore,

56 gallons = 1 minutes

13472.25792 gallons = ? minutes

number of minutes = 13472.25792 / 56

number of minutes = 240.576034286

number of minutes to drain the entire tower = 241 minutes (nearest minutes)