Question

ANSWER 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.

Answer 1

Answer:

241 minutes

Step-by-step explanation:

Given:

Height of cylinder, h = 15 ft

Radius, r = $\frac{d}{2} = \frac{12}{2} = 6$ (both cylinder and cone have same radius)

Let's find the height of cone, since angle of inclination = 25°C.

$tan25 = \frac{h}{r}$

$h = r tan25$

$h = 6 tan25 = 2.8$

Height of cone = 2.8 ft

Let's find colume of tower.

Volume = Volume of cone + volume of cylinder.

Formula for volume of cone = ⅓πr²h

Volume of cylinder = πr²h

Therefore,

V = ⅓πr²h + πr²h

V = ⅓π*6²*2.8 + π*6²*15

V = 105.558 + 1696.46

V = 1802.02 ft³

Since volume is 1802.02 ft³, and there are 7.48 gallons in a cubic ft, the total gallon =

1802.02 * 7.48 = 13479.11 gallons

Water is used at an average rate of 56 gallons per minute.

Amount if time to drain the water:

Total gallons / average rate

$= \frac{13479.11}{56} = 240.698$

≈ 241 minutes