Question

A water tank has the shape of an inverted right circular cone of altitude 12 ft and base radius of 6 ft . tif water is being pumped into the tank at a rate of 1 0 gal / min. how long will it take for the tank to fill?

Answer 1

To find the time it will take to fill the water tank, calculate the volume of the tank and divide it by the rate at which water is being pumped into the tank. The volume of a cone is (1/3) * π * r^2 * h. Convert the rate from gallons to cubic feet per minute and divide the volume by the rate.

Step-by-step explanation:

To find the time it will take to fill the water tank, we need to calculate the volume of the tank and then divide it by the rate at which water is being pumped into the tank.

The volume of a cone is given by the formula V = (1/3) * π * r2 * h, where r is the radius of the base and h is the altitude.

In this case, the radius (r) is given as 6 ft and the altitude (h) is given as 12 ft. Plugging these values into the formula, we get:

V = (1/3) * π * 62 * 12 = 144 π ft3

Next, we convert the rate at which water is being pumped into the tank from gallons per minute to cubic feet per minute. Since there are 7.48 gallons in 1 cubic foot, we have:

Rate = 10 gal/min * (1 ft3/7.48 gal) = 1.34 ft3/min

Finally, we divide the volume of the tank by the rate at which water is being pumped to find the time it will take to fill the tank:

Time = 144 π ft3 / 1.34 ft3/min ≈ 107.46 min